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A266822 Expansion of Product_{k>=1} ((1 + x^k) * (1 + 3*x^k)). 3

%I #7 Jan 04 2016 08:52:51

%S 1,4,7,20,35,60,124,200,324,524,865,1320,2016,3036,4453,6684,9668,

%T 13856,19792,27876,38956,54640,75320,103268,141191,191320,257892,

%U 346164,463284,615292,814883,1074556,1409904,1844284,2402756,3118020,4038164,5207344,6694116

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

%C Convolution of A000009 and A032308.

%H Vaclav Kotesovec, <a href="/A266822/b266822.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (4*sqrt(2*Pi) * n^(3/4)), where c = Pi^2/4 + log(3)^2/2 + polylog(2, -1/3) = 2.761842454190822171313479302500904035832... .

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

%Y Cf. A000009, A032308, A266819, A266820.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jan 04 2016

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