OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Bell Polynomial.
Wikipedia, Touchard polynomials.
FORMULA
a(0) = 1; a(n) = n*a(n-1) + n^3.
a(n) = n! + A337001(n).
E.g.f.: (1 + B_3(x) * exp(x)) / (1-x), where B_n(x) = Bell polynomials.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1+sum(k=0, 3, stirling(3, k, 2)*x^k)*exp(x))/(1-x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 04 2024
STATUS
approved