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Expansion of Product_{k>=0} (1+x^(4*k+1))^2.
2

%I #4 Aug 28 2015 03:14:49

%S 1,2,1,0,0,2,4,2,0,2,5,4,1,2,8,10,4,2,9,14,9,4,12,22,16,6,13,30,30,14,

%T 17,40,44,24,21,50,66,42,29,64,92,66,41,78,127,106,62,96,164,152,93,

%U 120,215,220,139,150,269,302,205,192,340,412,296,248,417

%N Expansion of Product_{k>=0} (1+x^(4*k+1))^2.

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

%t nmax=80; CoefficientList[Series[Product[(1+x^(4*k+1))^2, {k, 0, nmax}], {x, 0, nmax}], x]

%Y Cf. A169975, A261634, A261638.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Aug 27 2015