A258794 a(n) = [x^n] Product_{k=1..n} 1/(x^(2*k)*(1-x^k)^3).

1, 10, 294, 10592, 433350, 19269768, 910578172, 45070219993, 2313935076132, 122371149279812, 6631958513821919, 366896706349540194, 20656935779581469141, 1180759136663178459661, 68388869189063880001236, 4007252716834400744174729, 237231272998203169561835387

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2015

Keywords

• nonn

Crossrefs

Cf. A258788, A258789, A258790, A258791, A258792, A258793, A258795, A258796.

Programs

Mathematica

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

Formula

a(n) ~ c * d^n / n^3, where d = 70.2047644028747363037741119300640924984352825702388550206966992563459... = r^5/(r-1)^3, where r is the root of the equation polylog(2, 1-r) + (5*log(r)^2)/6 = 0, c = 4.0416205700754156... .