A258792 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)^3).

1, 6, 69, 915, 12978, 194688, 3051617, 49526487, 826910754, 14135805042, 246508115583, 4372617452085, 78714369892152, 1435357362134796, 26472477913596486, 493178852479545556, 9270953614684288962, 175695092091980786166, 3354069936616380522256

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) ~ c * d^n / n^3, where d = 22.0610202494679061193859054301626736218023392292898139172609021542610... = r^4/(r-1)^3, where r is the root of the equation polylog(2, 1-r) + (2*log(r)^2)/3 = 0, c = 20.953639522741... .

Mathematica

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

Crossrefs

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

Sequence in context: A201535 A198699 A346938 * A214694 A347674 A234509

Adjacent sequences: A258789 A258790 A258791 * A258793 A258794 A258795

Keyword

nonn

Author

Vaclav Kotesovec, Jun 10 2015

Status

approved