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 A292914 a(n) = n! * [x^n] exp(exp(n*x)-1). 8

%I

%S 1,1,8,135,3840,162500,9471168,722247211,69457674240,8192781080883,

%T 1159750000000000,193603940326506270,37568854100470136832,

%U 8372811803057822746561,2121274569058397526065152,605589097505502777099609375,193324500041805946527313559552,68549156597838159410025756211308

%N a(n) = n! * [x^n] exp(exp(n*x)-1).

%H Seiichi Manyama, <a href="/A292914/b292914.txt">Table of n, a(n) for n = 0..258</a>

%F a(n) = [x^n] 1/(1 - n*x/(1 - n*x/(1 - n*x/(1 - 2*n*x/(1 - n*x/(1 - 3*n*x/(1 - n*x/(1 - 4*n*x/(1 - ...))))))))), a continued fraction.

%F a(n) = exp(-1)*n^n*Sum_{k>=0} k^n/k!.

%F a(n) = A292913(n,n).

%F a(n) = n^n * Bell(n). - _Alois P. Heinz_, Sep 26 2017

%p a:= n-> n^n * combinat[bell](n):

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Sep 26 2017

%t Table[n! SeriesCoefficient[Exp[Exp[n x] - 1], {x, 0, n}], {n, 0, 17}]

%t Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-((-1)^(k + 1) (k - 1) + k + 3) n x/4, 1, {k, 0, n}]), {x, 0, n}], {n, 0, 17}]

%t Join[{1}, Table[n^n BellB[n], {n, 1, 17}]]

%Y Main diagonal of A292913.

%Y Cf. A000110.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Sep 26 2017

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Last modified August 3 04:47 EDT 2021. Contains 346435 sequences. (Running on oeis4.)