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A317362 Expansion of e.g.f. exp(exp(x/(1 + x)) - 1). 0
1, 1, 0, -1, 3, -8, 23, -89, 556, -4773, 44425, -397670, 3060577, -12448655, -235761640, 9571505555, -241952653453, 5424619822460, -116900288145113, 2494797839905055, -53406941947725348, 1152770311462756071, -25109138533156554399, 550613923917090815374, -12088287036694435407999 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Inverse Lah transform of the Bell numbers (A000110).

LINKS

Table of n, a(n) for n=0..24.

N. J. A. Sloane, Transforms

FORMULA

a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n-1,k-1)*Bell(k)*n!/k!, where Bell() = A000110.

MAPLE

a:= proc(n) option remember; add((-1)^(n-k)*n!/k!*

      binomial(n-1, k-1)*combinat[bell](k), k=0..n)

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Jul 26 2018

MATHEMATICA

nmax = 24; CoefficientList[Series[Exp[Exp[x/(1 + x)] - 1], {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[(-1)^(n - k) Binomial[n - 1, k - 1] BellB[k] n!/k!, {k, 0, n}], {n, 0, 24}]

CROSSREFS

Cf. A000110, A084357.

Sequence in context: A148780 A148781 A327151 * A309114 A065083 A280190

Adjacent sequences:  A317359 A317360 A317361 * A317363 A317364 A317365

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jul 26 2018

STATUS

approved

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Last modified May 26 17:16 EDT 2022. Contains 354092 sequences. (Running on oeis4.)