A258789 a(n) = [x^n] Product_{k=1..n} 1/(x^(2*k)*(1-x^k)).

1, 1, 5, 27, 169, 1115, 7760, 55748, 411498, 3101490, 23785645, 185064559, 1457664666, 11602828475, 93205739436, 754751603157, 6155229065861, 50515624923790, 416930705579538, 3458726257239312, 28825340825747729, 241245120218823892, 2026803168946440648

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..380

Crossrefs

Cf. A258268, A258788, A258791, A258793, A258794.

Programs

Maple

T:=proc(n, k) option remember; `if`(n=0 or k=1, 1, T(n, k-1) + `if`(n
				

Mathematica

Table[SeriesCoefficient[1/Product[x^(2*k)*(1-x^k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}], {x, 0, n*(n+2)}], {n, 0, 30}]

Formula

a(n) ~ c * d^n / n^2, where d = A258268 = 9.15337019245412246194853029240135454007332720412184884968926320147613... = r^3/(r-1), where r is the root of the equation polylog(2, 1-r) + 3*log(r)^2/2 = 0, c = 0.8069142856822510276258439534144172057548... .