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A304878
G.f.: Sum_{k>=0} q(k)^3 * x^k / Sum_{k>=0} q(k)*x^k, where q(n) is A000009(n).
5
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
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 20 2018
STATUS
approved