A294499 Inverse binomial transform of the number of overpartitions (A015128).

1, 1, 1, 1, -1, 3, -5, 7, -7, 3, 5, -9, -17, 129, -417, 977, -1809, 2591, -2317, -1061, 10485, -27983, 49165, -51319, -26861, 311455, -1011473, 2393275, -4643591, 7521265, -9694135, 7738137, 4976985, -38789975, 106112817, -215068927, 354515933, -464539803

Offset: 0

Author

Vaclav Kotesovec, Nov 01 2017

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A266497, A281425, A293467.

Programs

Mathematica

Table[Sum[(-1)^(n-k)*Binomial[n, k]*Sum[PartitionsP[k-j]*PartitionsQ[j], {j, 0, k}], {k, 0, n}], {n, 0, 50}]

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A015128(k).

a(n) = [x^n] (1 - x)^n/theta_4(x), where theta_4() is the Jacobi theta function. - Ilya Gutkovskiy, Nov 03 2017