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Expansion of Product_{k>=0} (1+x^(3*k+1))^3.
1

%I #4 Aug 28 2015 03:15:24

%S 1,3,3,1,3,9,9,6,12,18,15,21,37,36,33,55,69,66,90,117,111,136,195,204,

%T 217,294,330,342,447,531,541,657,804,839,978,1215,1288,1419,1755,1936,

%U 2094,2535,2846,3027,3588,4123,4392,5073,5869,6261,7080

%N Expansion of Product_{k>=0} (1+x^(3*k+1))^3.

%F a(n) ~ exp(Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)).

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

%Y Cf. A261612, A261615, A261634.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Aug 27 2015