A265841 Expansion of Product_{k>=1} (1 + k^4*x^k).

1, 1, 16, 97, 337, 2177, 7313, 38529, 108594, 717186, 2053522, 7527458, 30757155, 88042387, 448973459, 1390503396, 4087546309, 12699966117, 49599776261, 124699632310, 608410782855, 1651128186296, 4862631132392, 13170300313769, 39285370060347, 130999461143020

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, A265838, A265840, A265842.

Column k=4 of A292189.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[1 + k^4*x^k, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*j^(4*k)*x^(j*k)/k). - Ilya Gutkovskiy, Jun 14 2018

Conjecture: log(a(n)) ~ 4*sqrt(n/2) * (log(2*n) - 2). - Vaclav Kotesovec, Dec 27 2020