A265842 Expansion of Product_{k>=1} (1 + k^5*x^k).

1, 1, 32, 275, 1267, 11925, 51445, 406183, 1406614, 14690040, 51144366, 251885088, 1481359033, 5108404955, 42614629915, 158222158038, 588574803125, 2360755022421, 13255325882835, 39266011999104, 325719196861377, 1031732678138822, 3791401325667894

Offset: 0

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A022629, A092484, A265839, A265840, A265841.

Column k=5 of A292189.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[1 + k^5*x^k, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*j^(5*k)*x^(j*k)/k). - Ilya Gutkovskiy, Oct 18 2018

Conjecture: log(a(n)) ~ 5*sqrt(n/2) * (log(2*n) - 2). - Vaclav Kotesovec, Dec 27 2020