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%I #10 Jan 10 2017 04:58:39
%S 1,2,4,8,14,24,39,62,96,146,218,320,463,662,936,1310,1816,2496,3404,
%T 4608,6196,8278,10994,14520,19076,24938,32448,42032,54218,69656,89149,
%U 113680,144456,182952,230966,290688,364774,456446,569600,708938,880128,1089984
%N Expansion of Product_{k>=1} (1 - x^(6*k)) * (1 + x^k) / (1 - x^k).
%C Convolution of A219601 and A000009.
%H Vaclav Kotesovec, <a href="/A280874/b280874.txt">Table of n, a(n) for n = 0..2000</a>
%H Andrew Sills, <a href="http://home.dimacs.rutgers.edu/~asills/EMDC/SillsEMDC-Rev.pdf">Towards an Automation of the Circle Method</a>, Gems in Experimental Mathematics in Contemporary Mathematics, 2010.
%F a(n) ~ Pi*sqrt(2) * BesselI(1, sqrt(8*n+2)*Pi/3) / (3*sqrt(12*n+3)).
%F a(n) ~ exp(2*Pi*sqrt(2*n)/3) / (6*2^(3/4)*n^(3/4)) * (1 + (Pi/6 - 9/(16*Pi))/sqrt(2*n) + (Pi^2/144 - 135/(1024*Pi^2) - 15/64)/n).
%t nmax = 60; CoefficientList[Series[Product[(1-x^(6*k))*(1+x^k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000009, A219601.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jan 09 2017
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