A304460 Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^(n^3).

1, 1, 44, 4410, 905840, 318906400, 172185088824, 132357574570221, 137406570363495360, 185242628827767255255, 314645673306845990409300, 657405676947400829561901359, 1656968286301847988118098735168, 4957425610652588047512198547937050

Offset

0,3

Comments

In general, for m>=3, coefficient of x^n in Product_{k>=1} 1/(1-x^k)^(n^m) is asymptotic to n^(m*n)/n!.

Links

Table of n, a(n) for n=0..13.

Formula

a(n) ~ exp(n) * n^(2*n - 1/2) / sqrt(2*Pi).

Mathematica

nmax = 20; Table[SeriesCoefficient[Product[1/(1-x^k)^(n^3), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
nmax = 20; Table[SeriesCoefficient[1/QPochhammer[x]^(n^3), {x, 0, n}], {n, 0, nmax}]

Crossrefs

Cf. A008485, A023872, A304446, A304459.

Sequence in context: A282186 A200899 A220599 * A332562 A078279 A268548

Adjacent sequences: A304457 A304458 A304459 * A304461 A304462 A304463

Keyword

nonn

Author

Vaclav Kotesovec, May 13 2018

Status

approved