OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Bell Polynomial
FORMULA
a(n) = n! * [x^n] exp(n*(1 + x - exp(x))).
a(n) = Sum_{k=0..n} binomial(n,k) * BellPolynomial_k(-n) * n^(n-k).
MATHEMATICA
Table[n! SeriesCoefficient[Exp[n (1 + x - Exp[x])], {x, 0, n}], {n, 0, 20}]
Join[{1}, Table[Sum[Binomial[n, k] BellB[k, -n] n^(n - k), {k, 0, n}], {n, 1, 20}]]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 19 2020
STATUS
approved