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%I #22 Jan 09 2019 09:14:22
%S 1,2,9,54,404,3598,37003,430300,5571147,79358032,1231990840,
%T 20684884234,373208232229,7197079035318,147658793214733,
%U 3210107125516682,73690798853163884,1780718798351625094,45171972342078432287,1199948465249850848608,33305064129201851432591,963911863209583899492324
%N Expansion of e.g.f. exp(exp(x)/(1 - x) - 1).
%F a(0) = 1; a(n) = Sum_{k=1..n} A000522(k)*binomial(n-1,k-1)*a(n-k).
%F a(n) ~ exp(-exp(1)/2 - 3/4 + 2*exp(1/2)*sqrt(n) - n) * n^(n - 1/4) / sqrt(2). - _Vaclav Kotesovec_, Dec 19 2018
%p seq(n!*coeff(series(exp(exp(x)/(1 - x) - 1), x=0, 22), x, n), n=0..21); # _Paolo P. Lava_, Jan 09 2019
%t nmax = 21; CoefficientList[Series[Exp[Exp[x]/(1 - x) - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t a[n_] := a[n] = Sum[Floor[Exp[1] k!] Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 21}]
%Y Cf. A000262, A000522, A318364, A321989.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Dec 19 2018
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