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%I #9 Mar 31 2018 06:56:19
%S 1,1,2,6,9,19,36,62,110,197,332,559,947,1548,2538,4133,6610,10536,
%T 16710,26191,40879,63465,97732,149852,228658,346788,523694,787503,
%U 1178325,1756294,2607686,3855676,5680851,8341007,12202794,17795283,25869297,37487313
%N Expansion of Product_{k>=1} (1 + x^k)^A002131(k).
%H Vaclav Kotesovec, <a href="/A301798/b301798.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ exp(3^(4/3) * Pi^(2/3) * Zeta(3)^(1/3) * n^(2/3) / 2^(7/3) - Pi^(4/3) * n^(1/3) / (2^(8/3) * 3^(4/3) * Zeta(3)^(1/3)) - Pi^2 / (2592 * Zeta(3))) * Zeta(3)^(1/6) / (2^(7/6) * 3^(1/3) * Pi^(1/6) * n^(2/3)).
%t nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[DivisorSum[k, # / GCD[#, 2] &] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 31 2018 *)
%Y Cf. A000203, A002131, A192065.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 26 2018
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