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%I #7 Mar 31 2018 06:45:01
%S 1,1,3,7,13,27,55,99,185,341,604,1064,1863,3181,5411,9123,15167,25051,
%T 41083,66715,107703,172735,275034,435484,685753,1073481,1672160,
%U 2592070,3998278,6140196,9389302,14296376,21682534,32759202,49308812,73956692,110545113
%N Expansion of Product_{k>=1} (1 + x^k)^A001615(k), where A001615 is the Dedekind psi function.
%H Vaclav Kotesovec, <a href="/A301594/b301594.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ exp(3^(5/3) * (5*Zeta(3))^(1/3) * n^(2/3) / (2^(4/3) * Pi^(2/3)) - Pi^(2/3) * n^(1/3) / (2^(5/3) * 3^(2/3) * (5*Zeta(3))^(1/3)) - Pi^2 / (2160 * Zeta(3))) * (5*Zeta(3))^(1/6) / (2^(3/4) * 3^(1/6) * Pi^(5/6) * n^(2/3)).
%t nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[k*Sum[MoebiusMu[d]^2 / 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. A001615, A156303.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 24 2018
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