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%I #5 Nov 08 2017 12:38:29
%S 1,0,0,1,0,3,0,6,3,10,9,15,28,24,60,47,126,99,227,225,414,498,717,
%T 1044,1301,2082,2364,3984,4482,7353,8513,13287,16317,23698,30789,
%U 42081,57499,74763,105276,133273,190155,238122,338291,425775,596142,759651,1041498
%N Expansion of Product_{k>=1} (1 + x^(2*k-1))^(k*(k-1)/2).
%F a(n) ~ exp(Pi*14^(1/4) * n^(3/4) / (3^(5/4) * 5^(1/4)) - Pi*5^(1/4) * n^(1/4) / (2^(17/4) * 3^(3/4) * 7^(1/4))) * 7^(1/8) / (2^(19/8) * 15^(1/8) * n^(5/8)).
%t nmax = 50; CoefficientList[Series[Product[(1+x^(2*k-1))^(k*(k-1)/2), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A027998, A027999, A263140, A294749.
%K nonn
%O 0,6
%A _Vaclav Kotesovec_, Nov 08 2017
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