A379991 Expansion of e.g.f. exp(-x)/(exp(-x) - x)^3.

1, 5, 34, 293, 3052, 37247, 520918, 8211065, 143997160, 2780465147, 58611713434, 1339236707525, 32969142927580, 869913580853735, 24490615055384062, 732751463209179953, 23217990692393685712, 776689510407852177011, 27353286267329098887202

Offset

0,2

Links

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

Formula

a(n) = n! * Sum_{k=0..n} (k+2)^(n-k) * binomial(k+2,2)/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (k+2)^(n-k)*binomial(k+2, 2)/(n-k)!);

Crossrefs

Cf. A377530, A379942, A379990.

Sequence in context: A380619 A379203 A259906 * A355258 A334066 A330649

Adjacent sequences: A379988 A379989 A379990 * A379992 A379993 A379994

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 07 2025

Status

approved