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%I #4 Aug 28 2015 03:16:36
%S 1,4,6,4,1,4,16,24,16,8,22,48,52,32,38,92,128,96,70,140,245,244,172,
%T 228,417,488,374,380,680,924,798,676,1044,1560,1542,1256,1625,2524,
%U 2778,2304,2537,3892,4716,4156,4076,5908,7650,7196,6592,8796,11938
%N Expansion of Product_{k>=0} (1+x^(4*k+1))^4.
%C In general, if j > 0, a > 0, b > 0, GCD(a,b) = 1 and g.f. = Product_{k>=0} (1 + x^(a*k+b))^j, then a(n) ~ 2^((j-3)/2 - j*b/a) * j^(1/4) * exp(Pi*sqrt(j*n/(3*a))) / ((3*a)^(1/4) * n^(3/4)).
%F a(n) ~ exp(Pi*sqrt(n/3)) / (sqrt(2) * 3^(1/4) * n^(3/4)).
%t nmax=50; CoefficientList[Series[Product[(1+x^(4*k+1))^4, {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A261612, A261615, A261637, A169975, A261630, A261634.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Aug 27 2015
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