A379994 Expansion of e.g.f. exp(-3*x)/(exp(-x) - x)^4.

1, 5, 37, 349, 3969, 52641, 796069, 13502693, 253667297, 5225690017, 117090480021, 2834363683317, 73697918467105, 2048252470006913, 60587779740857573, 1900347489736371301, 62992469337321611073, 2200238756416513719489, 80765631192992760237205

Offset

0,2

Links

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

Formula

a(n) = n! * Sum_{k=0..n} (k+1)^(n-k) * binomial(k+3,3)/(n-k)!.

a(n) == 1 (mod 4).

Prog

(PARI) a(n) = n!*sum(k=0, n, (k+1)^(n-k)*binomial(k+3, 3)/(n-k)!);

Crossrefs

Cf. A379943, A379993, A379995, A379996.

Sequence in context: A246540 A365842 A177395 * A370343 A258296 A197713

Adjacent sequences: A379991 A379992 A379993 * A379995 A379996 A379997

Keyword

nonn,easy,new

Author

Seiichi Manyama, Jan 07 2025

Status

approved