A304878 G.f.: Sum_{k>=0} q(k)^3 * x^k / Sum_{k>=0} q(k)*x^k, where q(n) is A000009(n).

1, 0, 0, 6, 0, 18, 30, 60, 66, 258, 402, 606, 1266, 1866, 3744, 6864, 9648, 15432, 30510, 41166, 72342, 118140, 178800, 266262, 441462, 652164, 1006410, 1567692, 2309958, 3385554, 5321838, 7530462, 11128440, 16799958, 23916474, 35123964, 51357318, 72495126

Offset

0,4

Comments

In general, if m > 1 and g.f. = Sum_{k>=0} q(k)^m * x^k / Sum_{k>=0} q(k)*x^k, then a(n, m) ~ exp(Pi*sqrt((m^2 - 1)*n/3)) * (m^2 - 1)^(3*m/4 - 1/2) / (2^(2*m - 1/2) * 3^(m/4) * m^(3*m/2 - 1) * n^(3*m/4)).

Links

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

Formula

a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (81*6^(1/4)*n^(9/4)).

Mathematica

nmax = 50; CoefficientList[Series[Sum[PartitionsQ[k]^3*x^k, {k, 0, nmax}] / Sum[PartitionsQ[k]*x^k, {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000009, A260664, A304873, A304877.

Sequence in context: A019134 A167298 A242838 * A167356 A219540 A292497

Adjacent sequences: A304875 A304876 A304877 * A304879 A304880 A304881

Keyword

nonn

Author

Vaclav Kotesovec, May 20 2018

Status

approved