Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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