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%I #8 Mar 31 2018 07:06:53
%S 1,1,4,12,30,78,184,448,1033,2361,5292,11676,25382,54470,115508,
%T 242132,502520,1032632,2103172,4246948,8507968,16915536,33391788,
%U 65470332,127539321,246928233,475274592,909658536,1731703788,3279644604,6180528236
%N Expansion of Product_{k>=1} 1/(1 - x^k)^A007434(k).
%C Euler transform of A007434.
%H Vaclav Kotesovec, <a href="/A301875/b301875.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ exp(4*Pi*n^(3/4) / (3^(5/4) * (5*Zeta(3))^(1/4)) + Zeta(3) / (2*Pi^2)) / (2^(3/2) * (15*Zeta(3))^(1/8) * n^(5/8)).
%t nmax = 40; CoefficientList[Series[Exp[Sum[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, A061255, A301876.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 28 2018
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