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%I #7 Aug 26 2015 16:17:30
%S 1,2,1,0,2,4,2,2,5,4,3,8,10,6,9,14,11,14,22,18,17,30,32,28,41,46,39,
%T 54,68,60,73,94,85,96,131,128,130,170,175,176,229,246,237,294,330,320,
%U 386,446,430,492,582,578,642,762,763,818,977,1008,1061,1254,1311
%N Expansion of Product_{k>=0} (1 + x^(3*k+1))^2.
%C Self-convolution of A261612.
%C In general, if a > 0, b > 0, GCD(a,b) = 1 and g.f. = Product_{k>=0} (1 + x^(a*k+b))^2, then a(n) ~ exp(Pi*sqrt(2*n/(3*a))) / (2^(2*b/a + 1/4) * 3^(1/4) * a^(1/4) * n^(3/4)).
%F a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(11/12) * sqrt(3) * n^(3/4)).
%t nmax = 60; CoefficientList[Series[Product[(1 + x^(3*k+1))^2, {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A022567, A035382, A261610, A261612, A261616.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 26 2015