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%I #16 Aug 09 2018 09:47:26
%S 1,1,6,95,3043,167342,14175447,1715544861,280986929888,59828264507385,
%T 16056622678756319,5300955907062294008,2110872493413444115109,
%U 997542435957462115205773,551887323312314977683048334,353334615697796170374209624907,259179558930246734075836153918127
%N E.g.f.: exp( Sum_{n>=1} (exp(n*x) - 1)^n / n ).
%C Compare to: exp( Sum_{n>=1} (exp(x) - 1)^n/n ) = 1/(2-exp(x)), the e.g.f. of Fubini numbers (A000670).
%H Vaclav Kotesovec, <a href="/A243802/b243802.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ c * d^n * (n!)^2 / n^(3/2), where d = A317855 = (1+exp(1/r))*r^2 = 3.161088653865428813830172202588132491..., r = 0.873702433239668330496568304720719298... is the root of the equation exp(1/r)/r + (1+exp(1/r)) * LambertW(-exp(-1/r)/r) = 0, and c = 0.37498840921734807101035131780130551... . - _Vaclav Kotesovec_, Aug 21 2014
%e E.g.f.: A(x) = 1 + x + 6*x^2/2! + 95*x^3/3! + 3043*x^4/4! + 167342*x^5/5! +...
%o (PARI) {a(n) = n!*polcoeff( exp( sum(m=1,n+1, (exp(m*x +x*O(x^n)) - 1)^m / m) ), n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A244585, A244437.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 21 2014
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