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Expansion of Product_{k>=1} 1/(1-x^(k^2))^(k^2).
6

%I #12 Sep 02 2017 04:04:42

%S 1,1,1,1,5,5,5,5,15,24,24,24,44,80,80,80,131,221,266,266,386,566,746,

%T 746,990,1474,1924,2089,2529,3709,4609,5269,6130,8576,11096,12746,

%U 14937,19397,25697,28997,34111,43135,56365,65905,76219,95770,120070,144370,163661

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

%H Vaclav Kotesovec, <a href="/A291655/b291655.txt">Table of n, a(n) for n = 0..10000</a>

%F log(a(n)) ~ 5 * Pi^(1/5) * Zeta(5/2)^(2/5) * n^(3/5) / (2^(6/5) * 3^(3/5)).

%t nmax = 100; CoefficientList[Series[Product[1/(1-x^(k^2))^(k^2), {k,1,nmax}], {x,0,nmax}], x]

%Y Cf. A001156, A033461, A281790, A285047, A291649, A291696, A291720.

%K nonn

%O 0,5

%A _Vaclav Kotesovec_, Aug 28 2017