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A306045 Expansion of e.g.f. Product_{k>=1} (1 + (exp(x) - 1)^k) / (1 - (exp(x) - 1)^k). 9

%I #13 Feb 21 2024 10:54:09

%S 1,2,10,74,682,7562,98410,1463114,24367402,449039882,9069093610,

%T 199050295754,4713774570922,119735740542602,3246094020405610,

%U 93519923311825994,2852458136048627242,91805618091515859722,3108657616523130770410,110453876295411957125834

%N Expansion of e.g.f. Product_{k>=1} (1 + (exp(x) - 1)^k) / (1 - (exp(x) - 1)^k).

%C Convolution of A167137 and A305550.

%H Vaclav Kotesovec, <a href="/A306045/b306045.txt">Table of n, a(n) for n = 0..410</a>

%F a(n) = Sum_{k=0..n} Stirling2(n,k) * A015128(k) * k!.

%F a(n) ~ n! * exp(Pi^2 * (1 - log(2)) / (16*log(2)) + Pi * sqrt(n/(2*log(2)))) / (8*n*(log(2))^n).

%t nmax = 20; CoefficientList[Series[Product[(1 + (Exp[x] - 1)^k) / (1 - (Exp[x] - 1)^k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!

%Y Cf. A015128, A167137, A305550, A306046.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jun 18 2018

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)