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

0,4

Links

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

Formula

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

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]

Crossrefs

Cf. A000009, A054440, A304873, A304878.

Sequence in context: A145811 A131772 A363524 * A147980 A021493 A195395

Adjacent sequences: A304874 A304875 A304876 * A304878 A304879 A304880

Keyword

nonn

Author

Vaclav Kotesovec, May 20 2018

Status

approved