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 A292914 a(n) = n! * [x^n] exp(exp(n*x)-1). 8
 1, 1, 8, 135, 3840, 162500, 9471168, 722247211, 69457674240, 8192781080883, 1159750000000000, 193603940326506270, 37568854100470136832, 8372811803057822746561, 2121274569058397526065152, 605589097505502777099609375, 193324500041805946527313559552, 68549156597838159410025756211308 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..258 FORMULA 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. a(n) = exp(-1)*n^n*Sum_{k>=0} k^n/k!. a(n) = A292913(n,n). a(n) = n^n * Bell(n). - Alois P. Heinz, Sep 26 2017 MAPLE a:= n-> n^n * combinat[bell](n): seq(a(n), n=0..20); # Alois P. Heinz, Sep 26 2017 MATHEMATICA Table[n! SeriesCoefficient[Exp[Exp[n x] - 1], {x, 0, n}], {n, 0, 17}] 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}] Join[{1}, Table[n^n BellB[n], {n, 1, 17}]] CROSSREFS Main diagonal of A292913. Cf. A000110. Sequence in context: A069988 A229237 A291699 * A072072 A195614 A358958 Adjacent sequences: A292911 A292912 A292913 * A292915 A292916 A292917 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Sep 26 2017 STATUS approved

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Last modified December 9 14:59 EST 2022. Contains 358700 sequences. (Running on oeis4.)