A291720 Expansion of Product_{k>=1} 1/(1 - x^(k^3))^(k^3).

1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 45, 45, 45, 45, 45, 45, 45, 45, 165, 165, 165, 192, 192, 192, 192, 192, 522, 522, 522, 738, 738, 738, 738, 738, 1530, 1530, 1530, 2502, 2502, 2502, 2502, 2502, 4218, 4218, 4218, 7458, 7458, 7458, 7836, 7836

Offset

0,9

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

log(a(n)) ~ 7 * (Gamma(1/3) * Zeta(7/3))^(3/7) * n^(4/7) / (2^(8/7) * 3^(9/7)).

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1 - x^(k^3))^(k^3), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000219, A003108, A291655, A291692, A291721.

Sequence in context: A088471 A087416 A290546 * A290832 A290624 A290238

Adjacent sequences: A291717 A291718 A291719 * A291721 A291722 A291723

Keyword

nonn

Author

Vaclav Kotesovec, Aug 30 2017

Status

approved