A316159 Expansion of e.g.f. exp(exp(x*exp(-x)) - 1).

1, 1, 0, -4, -1, 47, 17, -1111, -12, 43476, -49665, -2391805, 7528897, 168436465, -1052303380, -14234148280, 161462347715, 1288890088835, -27585406164839, -91839429007223, 5125915000647712, -6443738757309888, -1013794188308572677, 6728499674632962055, 205866724424357904465

Offset: 0

Author

Ilya Gutkovskiy, Jun 25 2018

Keywords

• sign

Links

• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000110, A003725, A007550.

Programs

Maple

a:=series(exp(exp(x*exp(-x))-1),x=0,25): seq(n!*coeff(a, x, n), n=0..24); # Paolo P. Lava, Mar 26 2019

Mathematica

nmax = 24; CoefficientList[Series[Exp[Exp[x Exp[-x]] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[(-k)^(n - k) Binomial[n, k] BellB[k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 24}]

Formula

a(n) = Sum_{k=0..n} (-k)^(n-k)*binomial(n,k)*Bell(k), where Bell() = A000110.