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

Offset: 0

Author

Vaclav Kotesovec, Dec 30 2015

Keywords

• nonn

Links

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

Crossrefs

Cf. A015128, A218481, A266232, A294499.

Programs

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}]

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