A305350 G.f.: Sum_{k>=0} A000009(k)^2 * x^k / Sum_{k>=0} A000041(k) * x^k.

1, 0, -1, 2, -1, 2, 4, 2, 0, 8, 13, 0, 14, 6, 23, 52, 14, 6, 96, 36, 72, 192, 98, 80, 219, 256, 246, 548, 456, 294, 971, 690, 488, 1790, 1164, 1752, 2914, 1654, 2180, 4488, 4020, 3742, 7546, 6040, 6537, 14916, 9256, 8990, 19142, 16216, 20190

Offset: 0

Author

Vaclav Kotesovec, May 31 2018

Keywords

• sign

Crossrefs

Cf. A000009, A000041, A304987, A304988.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Sum[PartitionsQ[k]^2*x^k, {k, 0, nmax}] / Sum[PartitionsP[k]*x^k, {k, 0, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(17/4) * 3^(1/4) * n^(5/4)).