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

0,2

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

Cf. A015128, A218481, A266232, A294499.

Sequence in context: A181137 A113041 A269650 * A291020 A282087 A238440

Adjacent sequences: A266494 A266495 A266496 * A266498 A266499 A266500

Keyword

nonn

Author

Vaclav Kotesovec, Dec 30 2015

Status

approved