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%I #11 Feb 28 2024 10:49:04
%S 1,2,6,32,196,1512,13384,135872,1545744,19441952,268386784,4018603008,
%T 65021744704,1127284876928,20880206388864,410781080941568,
%U 8561002328678656,188224613741879808,4355496092560324096,105752112730661347328,2688539359466319184896
%N Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(phi(k)/k), where phi is the Euler totient function A000010.
%C Convolution of A088009 and A000262.
%H Vaclav Kotesovec, <a href="/A318976/b318976.txt">Table of n, a(n) for n = 0..440</a>
%F E.g.f.: exp(x*(2 + x)/(1 - x^2)).
%F a(n) ~ 2^(-3/4) * 3^(1/4) * exp(sqrt(6*n) - n - 1/2) * n^(n - 1/4).
%t nmax = 20; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^(EulerPhi[k]/k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
%t nmax = 20; CoefficientList[Series[E^(x*(2 + x)/(1 - x^2)), {x, 0, nmax}], x] * Range[0, nmax]!
%Y Cf. A000262, A088009, A318814, A318977.
%Y Cf. A318975, A301555, A301554.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Sep 06 2018
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