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A258792 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)^3). 4
1, 6, 69, 915, 12978, 194688, 3051617, 49526487, 826910754, 14135805042, 246508115583, 4372617452085, 78714369892152, 1435357362134796, 26472477913596486, 493178852479545556, 9270953614684288962, 175695092091980786166, 3354069936616380522256 (list; graph; refs; listen; history; text; internal format)
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: A288719 A201535 A198699 * A214694 A234509 A177751

Adjacent sequences:  A258789 A258790 A258791 * A258793 A258794 A258795

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jun 10 2015

STATUS

approved

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)