%I #5 Dec 15 2015 18:59:00

%S 1,1,1,1,5,5,5,12,28,28,38,66,130,143,232,344,616,738,1094,1561,2840,

%T 3671,5117,7227,12833,16182,22428,32205,57058,71006,98684,141253,

%U 241563,301889,421994,610113,1018507,1278706,1784671,2549610,4224964,5333003,7491698

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

%H Vaclav Kotesovec, <a href="/A265821/b265821.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) ~ c * 2^(n/2), where

%F c = 4.633065657780064798394952757560310709647495826095820632429... if mod(n,4) = 0

%F c = 4.169885941972377533366541853673119715620037601993736640548... if mod(n,4) = 1

%F c = 4.088913297791237602600754017373520586356446410096065167531... if mod(n,4) = 2

%F c = 4.069986547973463713613958049535085419215417774875202440925... if mod(n,4) = 3.

%t nmax = 40; CoefficientList[Series[Product[1/(1 - (3*k-2)*x^(3*k-2)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A067553, A265820.

%K nonn

%O 0,5

%A _Vaclav Kotesovec_, Dec 15 2015