%I #9 May 29 2018 00:46:57

%S 1,1,9,45,201,819,3357,13329,52215,199686,750733,2774793,10112184,

%T 36357280,129131448,453379226,1574884565,5415956550,18450934294,

%U 62303210591,208624947952,693066815809,2285129922950,7480504628754,24320897894515,78557786077315

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

%C 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)).

%H Vaclav Kotesovec, <a href="/A255965/b255965.txt">Table of n, a(n) for n = 0..1000</a>

%H Vaclav Kotesovec, <a href="/A255965/a255965.txt">Asymptotic formula</a>

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

%t 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]

%Y Cf. A000041 (m=1), A000219 (m=2), A000294 (m=3), A000335 (m=4), A000391 (m=5), A000417 (m=6), A000428 (m=7).

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Mar 12 2015