A304877 G.f.: Sum_{k>=0} q(k)^2 * x^k / Sum_{k>=0} q(k)*x^k, where q(n) is A000009(n).

1, 0, 0, 2, 0, 4, 4, 8, 4, 20, 20, 28, 38, 52, 80, 128, 128, 176, 300, 316, 476, 648, 832, 972, 1428, 1720, 2340, 3014, 3844, 4588, 6556, 7476, 9760, 12588, 15596, 19480, 25140, 29796, 37728, 47604, 58140, 70856, 90148, 107692, 133228, 167284, 198692, 242728

Offset: 0

Author

Vaclav Kotesovec, May 20 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000009, A054440, A304873, A304878.

Programs

Mathematica

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

Formula

a(n) ~ sqrt(3) * exp(Pi*sqrt(n)) / (2^(11/2) * n^(3/2)).