A258791 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)^2).

1, 3, 20, 158, 1307, 11352, 102538, 954904, 9112038, 88723163, 878714118, 8829998320, 89848944237, 924291213496, 9600148608620, 100565064076006, 1061498376477423, 11281275452880277, 120635822090127386, 1297256892395670322, 14021436433125959714

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2015

Keywords

• nonn

Crossrefs

Cf. A258788, A258789, A258793, A258794.

Programs

Mathematica

Table[SeriesCoefficient[1/Product[x^k*(1-x^k)^2, {k, 1, n}], {x, 0, n}], {n, 0, 25}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}]^2, {x, 0, n*(n+3)/2}], {n, 0, 25}]

Formula

a(n) ~ c * d^n / n^(5/2), where d = 12.0708016857156441729965623654557363850943928675996965027830903372727... = r^3/(r-1)^2, where r is the root of the equation polylog(2, 1-r) + (3*log(r)^2)/4 = 0, c = 8.36819319541... .