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A294669 Expansion of Product_{k>=1} 1/(1 - x^(2*k-1))^(k*(3*k-1)/2). 4

%I

%S 1,1,1,6,6,18,33,55,115,185,373,604,1113,1903,3251,5678,9350,16153,

%T 26420,44561,72912,120150,196329,317988,516881,827778,1333570,2120492,

%U 3381947,5347513,8447482,13285450,20813814,32547272,50638328,78707858,121738479

%N Expansion of Product_{k>=1} 1/(1 - x^(2*k-1))^(k*(3*k-1)/2).

%H Vaclav Kotesovec, <a href="/A294669/b294669.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) ~ exp(2*Pi * n^(3/4) / (3*5^(1/4)) + Zeta(3) * sqrt(5*n) / Pi^2 + 5^(1/4) * (Pi/48 - 5*Zeta(3)^2 / Pi^5) * n^(1/4) + 100*Zeta(3)^3 / (3*Pi^8) + 17*Zeta(3) / (96*Pi^2) - 1/24) * sqrt(A) / (2^(101/48) * 5^(11/96) * Pi^(1/24) * n^(59/96)), where A is the Glaisher-Kinkelin constant A074962.

%t nmax = 50; CoefficientList[Series[Product[1/(1-x^(2*k-1))^(k*(3*k-1)/2),{k,1,nmax}],{x,0,nmax}],x]

%Y Cf. A035528, A262811, A294591, A278768.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Nov 06 2017

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