A277613 Logarithmic derivative of the g.f. of the solid partitions A000293.

1, 7, 19, 47, 76, 145, 183, 319, 433, 762, 1068, 1625, 1457, 511, -2696, -7617, -12494, -8999, 14802, 78682, 195984, 363458, 530289, 574297, 252976, -820475, -3259007, -7929105, -15918795, -27966750, -42783874, -52969921, -37772397, 47098898, 278012363, 759015293, 1583148046, 2729030066, 3860814119, 4015793914, 1214574612, -7871995868, -27884564061, -63760120938, -117678872282, -182313402679, -228194585696, -183355932567, 93528356566, 836233409412, 2360489258476, 4956621402741, 8577450776595, 12176709992155, 12572248705543, 2874527812671, -29026344726969, -100513507605919, -229939345736773, -423043591887710, -643162163240861, -757839109104688, -458886747576888, 831588355306815, 4020413344163097, 10249469548463477, 20417504944664974, 33937902760293134, 46224437161712292, 44445354551818961, 1635692222011481, -129140996172417587

Offset

1,2

Comments

Based on the solid partitions calculated by Suresh Govindarajan and listed in A000293.

Finding a formula for this sequence is an unsolved problem; at first it was thought to be A278403, where: Sum_{n>=1} A278403(n)*x^n/n = log( Product_{n>=1} 1/(1 - x^n)^(n*(n+1)/2) ).

Links

Paul D. Hanna, Table of n, a(n) for n = 1..72

Example

L.g.f.: L(x) = x + 7*x^2/2 + 19*x^3/3 + 47*x^4/4 + 76*x^5/5 + 145*x^6/6 + 183*x^7/7 + 319*x^8/8 + 433*x^9/9 + 762*x^10/10 + 1068*x^11/11 + 1625*x^12/12 +...
such that
exp(L(x)) = 1 + x + 4*x^2 + 10*x^3 + 26*x^4 + 59*x^5 + 140*x^6 + 307*x^7 + 684*x^8 + 1464*x^9 + 3122*x^10 + 6500*x^11 + 13426*x^12 +...+ A000293(n)*x^n +...

Crossrefs

Cf. A000293, A278403.

Sequence in context: A372881 A155415 A155273 * A278403 A143128 A238730

Adjacent sequences: A277610 A277611 A277612 * A277614 A277615 A277616

Keyword

sign

Author

Paul D. Hanna, Nov 20 2016

Status

approved