OFFSET
0,3
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*(exp(x) - 1) - x).
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * BellPolynomial_k(n).
MATHEMATICA
Table[n! SeriesCoefficient[Exp[n (Exp[x] - 1) - x], {x, 0, n}], {n, 0, 19}]
Table[Sum[(-1)^(n - k) Binomial[n, k] BellB[k, n], {k, 0, n}], {n, 0, 19}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 27 2020
STATUS
approved