A258793 a(n) = [x^n] Product_{k=1..n} 1/(x^(2*k)*(1-x^k)^2).

1, 4, 55, 896, 16494, 326422, 6812064, 147937628, 3315019979, 76184664934, 1787702723767, 42688437971038, 1034621287862521, 25398832816003228, 630502487733706193, 15805630063826901440, 399669931534045129915, 10184690536676439639278, 261340023300544414822171

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2015

Keywords

• nonn

Crossrefs

Cf. A258788, A258789, A258791, A258794.

Programs

Mathematica

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

Formula

a(n) ~ c * d^n / n^(5/2), where d = 29.1694173246928561008040480794933198469510496062455151175744673506960... = r^4/(r-1)^2, where r is the root of the equation polylog(2, 1-r) + log(r)^2 = 0, c = 2.0036140319464... .