OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..386
N. J. A. Sloane, Transforms
FORMULA
a(n) = Sum_{k=0..n} binomial(n,k)*n^(n-k)*A000587(k).
a(n) ~ exp(1-exp(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-> abs(b(n, -n)):
seq(a(n), n=0..20); # Alois P. Heinz, Aug 04 2021
MATHEMATICA
Table[n! SeriesCoefficient[Exp[n x - Exp[x] + 1], {x, 0, n}], {n, 0, 20}]
Join[{1}, Table[Sum[Binomial[n, k] n^(n-k) BellB[k, -1] , {k, 0, n}], {n, 20}]]
PROG
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 50);
A298373:= func< n | Coefficient(R!(Laplace( Exp(-Exp(x)+n*x+1) )), n) >;
[A298373(n): n in [0..30]]; // G. C. Greubel, Jun 12 2024
(SageMath)
[factorial(n)*( exp(-exp(x) +n*x+1) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Jun 12 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 18 2018
STATUS
approved