A258790 a(n) = [x^n] Product_{k=1..n} 1/(x^(3*k)*(1-x^k)).

1, 1, 6, 48, 411, 3765, 36308, 363446, 3742085, 39405777, 422669224, 4603472960, 50790334667, 566603884871, 6381702580969, 72481863380510, 829331355150992, 9551576115706329, 110654552651370400, 1288710163262774157, 15080440970246785366, 177237948953055593475

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..338

Crossrefs

Cf. A258788, A258790, A258792, A258794, A258795, A258796.

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^(3*k)*(1-x^k), {k, 1, n}], {x, 0, n}], {n, 0, 25}]
Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}], {x, 0, n*(3*n+5)/2}], {n, 0, 25}]

Formula

a(n) ~ c * d^n / n^2, where d = 12.8718984948677835397002665286811919572579479691341210018008114644121... = r^4/(r-1), where r is the root of the equation polylog(2, 1-r) + 2*log(r)^2 = 0, c = 0.44720199058408831652920046766862756... .