A368725 - OEIS

A368725

a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^n / k!.

1, 1, 2, 9, 100, 1065, 10626, 224161, 4598504, 46288017, 2509940710, 84061763841, -1602021820596, 164372205860473, 5216105126641514, -883395389739028095, 79008645559978113616, -1023235751229436800735, -651030746777115881959602

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Bell Polynomial.

Wikipedia, Touchard polynomials

FORMULA

E.g.f.: Sum_{k>=0} (k * x)^k / (k! * (1 + k * x)).

a(n) = n! * [x^n] B_n(x) * exp(x) / (1+x), where B_n(x) = Bell polynomials.

PROG

(PARI) a(n) = n!*sum(k=0, n, (-1)^(n-k)*k^n/k!);

CROSSREFS

Main diagonal of A368724.

Cf. A256016.

Sequence in context: A357825 A187647 A322645 * A277180 A013520 A369673

Adjacent sequences: A368722 A368723 A368724 * A368726 A368727 A368728

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jan 04 2024

STATUS

approved