OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..368
Eric Weisstein's World of Mathematics, Bell Polynomial
FORMULA
a(n) = [x^n] (1/(1 - x)) * Sum_{k>=0} (n*x/(1 - x))^k / Product_{j=1..k} (1 - j*x/(1 - x)).
a(n) = n! * [x^n] exp(x + n*(exp(x) - 1)).
a(n) = Sum_{k=0..n} binomial(n,k) * BellPolynomial_k(n).
a(n) ~ exp((1/LambertW(1) - 2)*n) * n^n / (sqrt(1+LambertW(1)) * LambertW(1)^(n+1)). - Vaclav Kotesovec, Jun 08 2020
MATHEMATICA
Table[n! SeriesCoefficient[Exp[x + n (Exp[x] - 1)], {x, 0, n}], {n, 0, 18}]
Table[Sum[Binomial[n, k] BellB[k, n], {k, 0, n}], {n, 0, 18}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 19 2020
STATUS
approved