A305842 Product_{n>=1} (1 + x^n)^a(n) = g.f. of A000293 (solid partitions).

1, 4, 6, 14, 15, 26, 26, 48, 46, 83, 97, 146, 112, 49, -186, -448, -735, -485, 779, 3977, 9323, 16569, 23056, 23996, 10116, -31501, -120720, -283153, -548924, -932348, -1380125, -1655520, -1144651, 1384894, 7943203, 21083482, 42787785, 71816970, 98995196

Offset

1,2

Comments

Inverse weigh transform of A000293.

Links

Table of n, a(n) for n=1..39.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Solid Partition

Formula

Product_{n>=1} (1 + x^n)^a(n) = Sum_{k>=0} A000293(k)*x^k.

Example

(1 + x) * (1 + x^2)^4 * (1 + x^3)^6 * (1 + x^4)^14 * (1 + x^5)^15 * ... * (1 + x^n)^a(n) * ... = 1 + x + 4*x^2 + 10*x^3 + 26*x^4 + 59*x^5 + ... + A000293(k)*x^k + ...

Crossrefs

Cf. A000293, A001511, A037452, A193718, A305841.

Sequence in context: A310615 A310616 A310617 * A094298 A338045 A089226

Adjacent sequences: A305839 A305840 A305841 * A305843 A305844 A305845

Keyword

sign

Author

Ilya Gutkovskiy, Jun 11 2018

Status

approved