A294501 Inverse binomial transform of the number of planar partitions (A000219).

1, 0, 2, -1, 4, -7, 19, -48, 123, -304, 728, -1694, 3865, -8735, 19739, -44875, 102818, -236939, 546988, -1260023, 2888607, -6584008, 14927816, -33714166, 75976024, -171095098, 385405617, -868708176, 1959010348, -4417777937, 9957188242, -22420045445

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..3000

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000219(k).

G.f.: (1/(1 + x))*exp(Sum_{k>=1} sigma_2(k)*x^k/(k*(1 + x)^k)). - Ilya Gutkovskiy, Aug 20 2018

Mathematica

nmax = 40; s = CoefficientList[Series[Product[1/(1-x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x]; Table[Sum[(-1)^(n-k) * Binomial[n, k] * s[[k+1]], {k, 0, n}], {n, 0, nmax}]

Crossrefs

Cf. A281425, A293467, A294500, A294503, A294505.

Sequence in context: A364658 A184345 A045625 * A146004 A001933 A038557

Adjacent sequences: A294498 A294499 A294500 * A294502 A294503 A294504

Keyword

sign

Author

Vaclav Kotesovec, Nov 01 2017

Status

approved