A372348 a(n) = Sum_{j=0..n} p(n - j, j) where p(n, x) = Sum_{k=0..n} k! * Lah(n, k) * x^k where Lah = A271703.

1, 1, 2, 7, 40, 329, 3550, 47755, 777812, 15048925, 341018314, 8946278015, 268923178720, 9176058440977, 352386991982390, 15115253160180019, 719367763801641580, 37767206102310829445, 2176271214087106315042, 137024328250953628940455, 9388717924596833591237624

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Maple

Lah := (n, k) -> ifelse(n = k, 1, binomial(n-1, k-1)*n!/k!):
p := n -> local k; add(k!*Lah(n, k)*x^k, k = 0..n):
a := n -> local j; add(subs(x=j, p(n - j)), j = 0..n):
seq((a(n)), n = 0..21);

Crossrefs

Cf. A271703.

Sequence in context: A105625 A367255 A135082 * A102317 A361828 A031973

Adjacent sequences: A372345 A372346 A372347 * A372349 A372350 A372351

Keyword

nonn,changed

Author

Peter Luschny, Apr 28 2024

Status

approved