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A290219 a(n) = n! * [x^n] exp(exp(x) - n*x - 1). 7
1, 0, 2, -13, 127, -1573, 23711, -421356, 8626668, -199971255, 5177291275, -148078588667, 4636966634653, -157786054331852, 5797411243015250, -228749440644895405, 9646951350227609155, -433035586385769361001, 20614401475233006857035, -1037331650810058231498688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The n-th term of the n-th inverse binomial transform of A000110.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..386

N. J. A. Sloane, Transforms

FORMULA

a(n) ~ (-1)^n * exp(exp(-1) - 1) * n^n. - Vaclav Kotesovec, Aug 04 2021

MAPLE

b:= proc(n, k) option remember; `if`(n=0, 1,

      k*b(n-1, k)+ b(n-1, k+1))

    end:

a:= n-> b(n, -n):

seq(a(n), n=0..20);  # Alois P. Heinz, Aug 04 2021

MATHEMATICA

Table[n! SeriesCoefficient[Exp[Exp[x] - n x - 1], {x, 0, n}], {n, 0, 19}]

Join[{1}, Table[Sum[(-n)^(n - k) Binomial[n, k] BellB[k] , {k, 0, n}], {n, 1, 19}]]

CROSSREFS

Cf. A000110, A000296, A126617, A134980, A346738, A346739, A346740.

Sequence in context: A071362 A108471 A036078 * A057065 A259611 A351299

Adjacent sequences:  A290216 A290217 A290218 * A290220 A290221 A290222

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Oct 06 2017

STATUS

approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)