OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..200
Eric Weisstein's World of Mathematics, Bell Polynomial
FORMULA
a(n) = n! * [x^n] exp(n*(1 - exp(x)) - x).
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * BellPolynomial_k(-n).
MATHEMATICA
Table[n! SeriesCoefficient[Exp[n (1 - Exp[x]) - x], {x, 0, n}], {n, 0, 20}]
Table[Sum[(-1)^(n - k) Binomial[n, k] BellB[k, -n], {k, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 27 2020
STATUS
approved