A258795 a(n) = [x^n] Product_{k=1..n} 1/(x^(3*k)*(1-x^k)^2).

1, 5, 112, 3216, 104112, 3661517, 136580866, 5323418568, 214685704402, 8897404908604, 377068336570902, 16280261371485594, 714081427614467553, 31747177836376617322, 1428084942303149795972, 64902413675181889657064, 2976483322906106920966911

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2015

Keywords

• nonn

Crossrefs

Cf. A258788, A258790, A258791, A258792, A258793, A258794, A258796.

Programs

Mathematica

Table[SeriesCoefficient[1/Product[x^(3*k)*(1-x^k)^2, {k, 1, n}], {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}]^2, {x, 0, n*(3*n+5)/2}], {n, 0, 20}]

Formula

a(n) ~ c * d^n / n^(5/2), where d = 53.0676066669703028123492951828168330443393201750491213178019371417684... = r^5/(r-1)^2, where r is the root of the equation polylog(2, 1-r) + (5*log(r)^2)/4 = 0, c = 0.983501005499107... .