d   g   relation
2	2	15*e[1]
4	5	675*e[1]^2 + 9720*e[2]
4	4	1215*e[1]^2 + 12960*e[2]
4	3	3186*e[1]^2 + 21384*e[2]
4	2	22059*e[1]^2 + 66096*e[2]
6	8	50625*e[1]^3 + 2187000*e[1]*e[2] + 32221800*e[3]
6	7	81000*e[1]^3 + 2988900*e[1]*e[2] + 37470600*e[3]
6	6	148311*e[1]^3 + 4496472*e[1]*e[2] + 45868680*e[3]
6	5	(1328805*e[1]^3)/4 + (15669855*e[1]*e[2])/2 + 61024590*e[3]
6	4	1033965*e[1]^3 + 17453880*e[1]*e[2] + 94274280*e[3]
6	3	5991975*e[1]^3 + 62657550*e[1]*e[2] + 199527300*e[3]
6	2	169215075*e[1]^3 + 791256600*e[1]*e[2] + 1045240200*e[3]
8	11	5315625*e[1]^4 + 459270000*e[1]^2*e[2] + 3306744000*e[2]^2 + 13533156000*e[1]*e[3] + 298929657600*e[4]
8	10	8150625*e[1]^4 + 632772000*e[1]^2*e[2] + 4041576000*e[2]^2 + 16807240800*e[1]*e[3] + 331409232000*e[4]
8	9	(108226125*e[1]^4)/8 + 927725400*e[1]^2*e[2] + 5146120350*e[2]^2 + 21821831325*e[1]*e[3] + 375976792800*e[4]
8	8	(1219246425*e[1]^4)/49 + (72296971200*e[1]^2*e[2])/49 + (48467419200*e[2]^2)/7 + (1472426618400*e[1]*e[3])/49 + (3082074364800*e[4])/7
8	7	52509870*e[1]^4 + 2619335880*e[1]^2*e[2] + 10060666560*e[2]^2 + 44848838160*e[1]*e[3] + 539641025280*e[4]
8	6	(16783278813*e[1]^4)/125 + (678856907232*e[1]^2*e[2])/125 + (2044546588224*e[2]^2)/125 + (9388753978464*e[1]*e[3])/125 + (88558254965376*e[4])/125
8	5	(29207233125*e[1]^4)/64 + (113679658575*e[1]^2*e[2])/8 + (253327591125*e[2]^2)/8 + (1199418432975*e[1]*e[3])/8 + (8315954814825*e[4])/8
8	4	2459745225*e[1]^4 + 54451958400*e[1]^2*e[2] + 82559736000*e[2]^2 + 401491792800*e[1]*e[3] + 1860200899200*e[4]
8	3	(62932790025*e[1]^4)/2 + 431070822000*e[1]^2*e[2] + 388542420000*e[2]^2 + 1908591400800*e[1]*e[3] + 5039808530400*e[4]
8	2	3558482550945*e[1]^4 + 21953392584480*e[1]^2*e[2] + 8979926276160*e[2]^2 + 41593987179360*e[1]*e[3] + 43982076055680*e[4]
10	14	717609375*e[1]^5 + 103335750000*e[1]^3*e[2] + 2232052200000*e[1]*e[2]^2 + 4567440150000*e[1]^2*e[3] + 65771138160000*e[2]*e[3] + 201777518880000*e[1]*e[4] + 5915831150880000*e[5]
10	13	(2152828125*e[1]^5)/2 + 142947787500*e[1]^3*e[2] + 2827266120000*e[1]*e[2]^2 + 5852936880000*e[1]^2*e[3] + 76608991620000*e[2]*e[3] + 238398055308000*e[1]*e[4] + 6400097196192000*e[5]
10	12	(206527978125*e[1]^5)/121 + (2277519930000*e[1]^3*e[2])/11 + (448642492200000*e[1]*e[2]^2)/121 + (941295266982000*e[1]^2*e[3])/121 + (11054253400848000*e[2]*e[3])/121 + (34970008227840000*e[1]*e[4])/121 + (77170079941920000*e[5])/11
10	11	(5789787255*e[1]^5)/2 + 317163044016*e[1]^3*e[2] + 5075151010272*e[1]*e[2]^2 + 10812484120032*e[1]^2*e[3] + 112205561700960*e[2]*e[3] + 361677095819424*e[1]*e[4] + 7819575256886400*e[5]
10	10	5334217875*e[1]^5 + 520738470000*e[1]^3*e[2] + 7329609000000*e[1]*e[2]^2 + 15888261942000*e[1]^2*e[3] + 143100612144000*e[2]*e[3] + 471058174944000*e[1]*e[4] + 8907426281376000*e[5]
10	9	(11170258159725*e[1]^5)/1024 + (7466679619875*e[1]^3*e[2])/8 + (362821480142625*e[1]*e[2]^2)/32 + (1603637381878875*e[1]^2*e[3])/64 + (6134721534970875*e[2]*e[3])/32 + (20665333925861625*e[1]*e[4])/32 + (20890868292332325*e[5])/2
10	8	(428843025100575*e[1]^5)/16807 + (31501408674978000*e[1]^3*e[2])/16807 + (322635582041688000*e[1]*e[2]^2)/16807 + (728259712941114000*e[1]^2*e[3])/16807 + (4611791896415280000*e[2]*e[3])/16807 + (15921083858672448000*e[1]*e[4])/16807 + (214267355561561644800*e[5])/16807
10	7	71380891575*e[1]^5 + 4383479551500*e[1]^3*e[2] + 36747754218000*e[1]*e[2]^2 + 84841636005000*e[1]^2*e[3] + 430648936578000*e[2]*e[3] + 1524109892067000*e[1]*e[4] + 16477323974029800*e[5]
10	6	(800391250317267*e[1]^5)/3125 + (39652244489084976*e[1]^3*e[2])/3125 + (261775979836676928*e[1]*e[2]^2)/3125 + (618431657337757872*e[1]^2*e[3])/3125 + (483185649669593472*e[2]*e[3])/625 + (8748224707385689344*e[1]*e[4])/3125 + (2902175007973081344*e[5])/125
10	5	(1358932302552825*e[1]^5)/1024 + (6455240407468125*e[1]^3*e[2])/128 + (3979251045952875*e[1]*e[2]^2)/16 + (19204598570968125*e[1]^2*e[3])/32 + (3421122673255875*e[2]*e[3])/2 + (100748440083414375*e[1]*e[4])/16 + (75213108924119775*e[5])/2
10	4	12436110380925*e[1]^5 + 335573861742000*e[1]^3*e[2] + 1144496063592000*e[1]*e[2]^2 + 2801579057046000*e[1]^2*e[3] + 5410602553104000*e[2]*e[3] + 19922065623936000*e[1]*e[4] + 78044975036179200*e[5]
10	3	(1407843572418675*e[1]^5)/4 + 5890941082120500*e[1]^3*e[2] + 12263542081938000*e[1]*e[2]^2 + 29812360981599000*e[1]^2*e[3] + 34802753116320000*e[2]*e[3] + 123183166429260000*e[1]*e[4] + 270631226778670800*e[5]
10	2	158675761333525275*e[1]^5 + 1205523269376678000*e[1]^3*e[2] + 1185910493714856000*e[1]*e[2]^2 + 2657736739906038000*e[1]^2*e[3] + 1455285475386288000*e[2]*e[3] + 4483691818722144000*e[1]*e[4] + 3906294841734969600*e[5]
12	17	118405546875*e[1]^6 + 25575598125000*e[1]^4*e[2] + 1104865839000000*e[1]^2*e[2]^2 + 5303356027200000*e[2]^3 + 1507255249500000*e[1]^3*e[3] + 65113426778400000*e[1]*e[2]*e[3] + 479668910600880000*e[3]^2 + 99879871845600000*e[1]^2*e[4] + 1438270154576640000*e[2]*e[4] + 5856672839371200000*e[1]*e[5] + 213695549102407680000*e[6]
12	16	175240209375*e[1]^6 + 35464829400000*e[1]^4*e[2] + 1428959818440000*e[1]^2*e[2]^2 + 6364027232640000*e[2]^3 + 1967206806180000*e[1]^3*e[3] + 78906080860992000*e[1]*e[2]*e[3] + 542177800308144000*e[3]^2 + 122371994018736000*e[1]^2*e[4] + 1627918166109312000*e[2]*e[4] + 6708745374408000000*e[1]*e[5] + 227751563916898560000*e[6]
12	15	270641250000*e[1]^6 + 51005049975000*e[1]^4*e[2] + 1903526002620000*e[1]^2*e[2]^2 + 7803509582880000*e[2]^3 + 2647371570030000*e[1]^3*e[3] + 97830082650960000*e[1]*e[2]*e[3] + 622278679579920000*e[3]^2 + 153592766770608000*e[1]^2*e[4] + 1871114921070912000*e[2]*e[4] + 7815156762878784000*e[1]*e[5] + 244801823239454976000*e[6]
12	14	(74230805446875*e[1]^6)/169 + (168179813545590000*e[1]^4*e[2])/2197 + (5767797431282040000*e[1]^2*e[2]^2)/2197 + (21569809633827840000*e[2]^3)/2197 + (8113247609829516000*e[1]^3*e[3])/2197 + (273781771494561792000*e[1]*e[2]*e[3])/2197 + (1598217284406082032000*e[3]^2)/2197 + (435731951396594160000*e[1]^2*e[4])/2197 + (4812891055092489600000*e[2]*e[4])/2197 + (20404174052340429120000*e[1]*e[5])/2197 + (44929603751271402240000*e[6])/169
12	13	(24182201649375*e[1]^6)/32 + (241636924942875*e[1]^4*e[2])/2 + 3773277113933250*e[1]^2*e[2]^2 + 12740821803864000*e[2]^3 + 5374773327404250*e[1]^3*e[3] + 163952746889085000*e[1]*e[2]*e[3] + 869610561550731000*e[3]^2 + 264884260048947000*e[1]^2*e[4] + 2622848872025844000*e[2]*e[4] + 11303259254475804000*e[1]*e[5] + 292408041754759392000*e[6]
12	12	(20405082253917375*e[1]^6)/14641 + (2964888283307580000*e[1]^4*e[2])/14641 + (83440034656128360000*e[1]^2*e[2]^2)/14641 + (251404338948900480000*e[2]^3)/14641 + (120508873585177140000*e[1]^3*e[3])/14641 + (3284297644089712320000*e[1]*e[2]*e[3])/14641 + (15644833199928822960000*e[3]^2)/14641 + (5393945021940039600000*e[1]^2*e[4])/14641 + (47261657368180321920000*e[2]*e[4])/14641 + (207327672706819758912000*e[1]*e[5])/14641 + (434913377236699979520000*e[6])/1331
12	11	(3494048154873507*e[1]^6)/1250 + (45634547754945072*e[1]^4*e[2])/125 + (1143099827425715544*e[1]^2*e[2]^2)/125 + (3031589438098740288*e[2]^3)/125 + (1676036334199727808*e[1]^3*e[3])/125 + (40257501312901473216*e[1]*e[2]*e[3])/125 + (169890212972112538752*e[3]^2)/125 + (67299044355819505152*e[1]^2*e[4])/125 + (514026063800470222848*e[2]*e[4])/125 + (11490142719337904969424*e[1]*e[5])/625 + (46574172418401978239736*e[6])/125
12	10	6214407905475*e[1]^6 + 719983397826000*e[1]^4*e[2] + 15818683241592000*e[1]^2*e[2]^2 + 36341054652672000*e[2]^3 + 23575352965164000*e[1]^3*e[3] + 491108095336320000*e[1]*e[2]*e[3] + 1806580336519728000*e[3]^2 + 836616171360816000*e[1]^2*e[4] + 5473985284462464000*e[2]*e[4] + 24958463681475878400*e[1]*e[5] + 436174175050625088000*e[6]
12	9	(2060394985815895575*e[1]^6)/131072 + (26045610441671464875*e[1]^4*e[2])/16384 + (61638982842178751625*e[1]^2*e[2]^2)/2048 + (15044266621756015875*e[2]^3)/256 + (186955313981781547125*e[1]^3*e[3])/4096 + (51770779871698243125*e[1]*e[2]*e[3])/64 + (2604858121777831833375*e[3]^2)/1024 + (2878021373109641017875*e[1]^2*e[4])/2048 + (1975534050423807460125*e[2]*e[4])/256 + (73491558390349237925325*e[1]*e[5])/2048 + (1083048716145532246716375*e[6])/204814	20	23089081640625*e[1]^7 + 6982138288125000*e[1]^5*e[2] + 502713956745000000*e[1]^3*e[2]^2 + 7239080977128000000*e[1]*e[2]^3 + 514350853891875000*e[1]^4*e[3] + 44439913776258000000*e[1]^2*e[2]*e[3] + 319967379189057600000*e[2]^2*e[3] + 654748062970201200000*e[1]*e[3]^2 + 45445341689748000000*e[1]^3*e[4] + 1963238760997113600000*e[1]*e[2]*e[4] + 28925051078690807040000*e[3]*e[4] + 3997179212870844000000*e[1]^2*e[5] + 57559380665340153600000*e[2]*e[5] + 291694424524786483200000*e[1]*e[6] + 12727858319596662802560000*e[7]
14	19	33863986406250*e[1]^7 + 9697414289062500*e[1]^5*e[2] + 659113854399000000*e[1]^3*e[2]^2 + 8928199871791200000*e[1]*e[2]^3 + 679439634748875000*e[1]^4*e[3] + 55247146704149400000*e[1]^2*e[2]*e[3] + 372893104555171200000*e[2]^2*e[3] + 769501795876894080000*e[1]*e[3]^2 + 57003294126378600000*e[1]^3*e[4] + 2309845958182002240000*e[1]*e[2]*e[4] + 32067037438616980800000*e[3]*e[4] + 4748274081364413600000*e[1]^2*e[5] + 63898306053232210560000*e[2]*e[5] + 327129436344588958080000*e[1]*e[6] + 13427924938456150362240000*e[7]
14	18	(14857362254109375*e[1]^7)/289 + (235996274138625000*e[1]^5*e[2])/17 + (256203140915521800000*e[1]^3*e[2]^2)/289 + (3247451726339620800000*e[1]*e[2]^3)/289 + (266283579795207975000*e[1]^4*e[3])/289 + (20272217803846248240000*e[1]^2*e[2]*e[3])/289 + (127524519182804103360000*e[2]^2*e[3])/289 + (265626330376541294160000*e[1]*e[3]^2)/289 + (21121997432904688320000*e[1]^3*e[4])/289 + (798252880221426389760000*e[1]*e[2]*e[4])/289 + (10385658136994015715840000*e[3]*e[4])/289 + (1658326691558348491680000*e[1]^2*e[5])/289 + (20723896239702495840000000*e[2]*e[5])/289 + (107290521088274245962240000*e[1]*e[6])/289 + (242266702280068901635200000*e[7])/17
14	17	(41553882010265625*e[1]^7)/512 + (2632719973611853125*e[1]^5*e[2])/128 + (19642228235674419375*e[1]^3*e[2]^2)/16 + (57903033412601251875*e[1]*e[2]^3)/4 + (41198849403119533125*e[1]^4*e[3])/32 + (1459841678824141738125*e[1]^2*e[2]*e[3])/16 + (1062975905170650095625*e[2]^2*e[3])/2 + (2236990745446764181875*e[1]*e[3]^2)/2 + (1537339911581763914625*e[1]^3*e[4])/16 + (6730543795561497536625*e[1]*e[2]*e[4])/2 + 40783759951560420044250*e[3]*e[4] + 7072041521200670264250*e[1]^2*e[5] + 81497643316661428857000*e[2]*e[5] + 427114404825306492294000*e[1]*e[6] + 15230659733489368484316000*e[7]
14	16	133984056691485*e[1]^7 + 31698710880068232*e[1]^5*e[2] + 1757954471611770432*e[1]^3*e[2]^2 + 19158001517660189184*e[1]*e[2]^3 + (9308883846092574744*e[1]^4*e[3])/5 + (610151370838327334016*e[1]^2*e[2]*e[3])/5 + (3267670109868752620032*e[2]^2*e[3])/5 + (6954464706486564339072*e[1]*e[3]^2)/5 + 130005836149844438784*e[1]^3*e[4] + 4190007009667485726720*e[1]*e[2]*e[4] + (234880825195314603841536*e[3]*e[4])/5 + 8915785021653368931072*e[1]^2*e[5] + 94007270693471083812864*e[2]*e[5] + 499247495703113601540096*e[1]*e[6] + 16413465828593684202992640*e[7]
14	15	(79875271480826250*e[1]^7)/343 + (17535962514934041750*e[1]^5*e[2])/343 + (897639926520643020000*e[1]^3*e[2]^2)/343 + (8974851562825639920000*e[1]*e[2]^3)/343 + (960823003331431597500*e[1]^4*e[3])/343 + (57824716374740086200000*e[1]^2*e[2]*e[3])/343 + (5763939467058938880000*e[2]^2*e[3])/7 + (608483795894900948880000*e[1]*e[3]^2)/343 + (62380544987402670600000*e[1]^3*e[4])/343 + (1835353088496450974880000*e[1]*e[2]*e[4])/343 + (385489985307392908800000*e[3]*e[4])/7 + (3958279745314823042400000*e[1]^2*e[5])/343 + (5407724261400949927296000*e[2]*e[5])/49 + (203914341523799398103040000*e[1]*e[6])/343 + (125057365997593705378560000*e[7])/7
14	14	(159539747897935857375*e[1]^7)/371293 + (32280685835359977477000*e[1]^5*e[2])/371293 + (1513715250125700939240000*e[1]^3*e[2]^2)/371293 + (1059265428947802014400000*e[1]*e[2]^3)/28561 + (126078116981379944535000*e[1]^4*e[3])/28561 + (89825748061642936968240000*e[1]^2*e[2]*e[3])/371293 + (396534732382367828948160000*e[2]^2*e[3])/371293 + (865638177742508949591120000*e[1]*e[3]^2)/371293 + (98216902904300425808640000*e[1]^3*e[4])/371293 + (2614352554860269098740480000*e[1]*e[2]*e[4])/371293 + (24482114964148389308006400000*e[3]*e[4])/371293 + (5720000003173011732134112000*e[1]^2*e[5])/371293 + (49129953202299242440113408000*e[2]*e[5])/371293 + (268684344397903760756337600000*e[1]*e[6])/371293 + (43242391920550187874358080000*e[7])/2197
14	13	(217724017253467725*e[1]^7)/256 + (5035295280781440675*e[1]^5*e[2])/32 + (107217843454877029875*e[1]^3*e[2]^2)/16 + (219779998694386255125*e[1]*e[2]^3)/4 + (14692469069175022125*e[1]^4*e[3])/2 + (1452768773358905627625*e[1]^2*e[2]*e[3])/4 + 1434371852621017059750*e[2]^2*e[3] + 3175610521634877075750*e[1]*e[3]^2 + (6445960793555736828375*e[1]^3*e[4])/16 + (38412119592110688298875*e[1]*e[2]*e[4])/4 + 81003507779795682831750*e[3]*e[4] + (85330847065861891719225*e[1]^2*e[5])/4 + (651029731698357503016525*e[2]*e[5])/4 + (14468268211254595053941625*e[1]*e[6])/16 + (352159665938455124712587625*e[7])/16
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