A266497 - OEIS

A266497

Binomial transform of A015128.

1, 3, 9, 27, 79, 225, 627, 1717, 4633, 12341, 32501, 84737, 218959, 561263, 1428287, 3610671, 9072367, 22668285, 56345835, 139382713, 343242533, 841713531, 2055944117, 5003148987, 12132552115, 29323810757, 70651867863, 169719163521, 406541986857, 971192810019

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

FORMULA

a(n) ~ 2^(n-2) * exp(Pi*sqrt(n/2) + Pi^2/16) / n.

a(n) = [x^n] (1 + x)^n/theta_4(x), where theta_4() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 20 2018

MATHEMATICA

A015128[n_]:=Sum[PartitionsP[n-k]*PartitionsQ[k], {k, 0, n}];

Table[Sum[Binomial[n, k]*A015128[k], {k, 0, n}], {n, 0, 30}]

CROSSREFS