A255965 - OEIS

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A255965

Expansion of Product_{k>=1} 1/(1-x^k)^binomial(k+6,7).

1, 1, 9, 45, 201, 819, 3357, 13329, 52215, 199686, 750733, 2774793, 10112184, 36357280, 129131448, 453379226, 1574884565, 5415956550, 18450934294, 62303210591, 208624947952, 693066815809, 2285129922950, 7480504628754, 24320897894515, 78557786077315

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

In general, if g.f. = Product_{k>=1} 1/(1-x^k)^binomial(k+m-2,m-1) and m >= 1, then log(a(n)) ~ (m+1) * Zeta(m+1)^(1/(m+1)) * (n/m)^(m/(m+1)).

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Vaclav Kotesovec, Asymptotic formula

FORMULA

G.f.: exp(Sum_{k>=1} x^k/(k*(1 - x^k)^8)). - Ilya Gutkovskiy, May 28 2018

MATHEMATICA

nmax=40; CoefficientList[Series[Product[1/(1-x^k)^(k*(k+1)*(k+2)*(k+3)*(k+4)*(k+5)*(k+6)/7!), {k, 1, nmax}], {x, 0, nmax}], x]