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Expansion of Product_{k>=1} (1 + x^(3*k-2))^(3*k-2).
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%I #5 Oct 06 2015 16:18:10

%S 1,1,0,0,4,4,0,7,13,6,10,38,32,17,74,103,59,139,266,191,247,593,581,

%T 513,1175,1487,1190,2223,3453,2938,4158,7264,7095,8052,14430,16308,

%U 16246,27364,35347,34096,50997,72595,72163,94707,142522,151435,178047,270112

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

%H Alois P. Heinz, <a href="/A262949/b262949.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(3 * 2^(-4/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (2^(7/12) * sqrt(3*Pi) * n^(2/3)).

%t nmax=60; CoefficientList[Series[Product[(1 + x^(3*k-2))^(3*k-2),{k,1,nmax}],{x,0,nmax}],x]

%Y Cf. A261612, A262879, A262884, A262924, A262948.

%K nonn

%O 0,5

%A _Vaclav Kotesovec_, Oct 05 2015