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%I #9 Mar 31 2018 07:06:45
%S 1,1,3,11,23,63,137,329,738,1618,3562,7578,16116,33540,69384,141608,
%T 286493,574173,1140355,2247835,4394415,8532983,16450061,31513869,
%U 59991541,113536117,213659967,399910311,744672519,1379758479,2544367633
%N Expansion of Product_{k>=1} (1 + x^k)^A007434(k).
%H Vaclav Kotesovec, <a href="/A301876/b301876.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ exp(2^(5/4) * Pi / 3^(5/4) * (7/(5*Zeta(3)))^(1/4) * n^(3/4)) *(7/(15*Zeta(3)))^(1/8) / (2^(15/8) * n^(5/8)).
%t nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[Sum[d^2 MoebiusMu[k/d], {d, Divisors @ k}] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 31 2018 *)
%Y Cf. A007434, A299069, A301875.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 28 2018
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