A344317 a(n) = n*a(n-1) + n^(1+n mod 2), a(0) = 1.

1, 2, 6, 19, 80, 401, 2412, 16885, 135088, 1215793, 12157940, 133737341, 1604848104, 20863025353, 292082354956, 4381235324341, 70099765189472, 1191696008221025, 21450528147978468, 407560034811590893, 8151200696231817880, 171175214620868175481

Offset: 0

Author

Alois P. Heinz, May 14 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A155521, A174548, A344229, A344262.

Programs

Maple

a:= proc(n) a(n):= n*a(n-1) + n^(1+n mod 2) end: a(0):= 1:
seq(a(n), n=0..23);

Formula

E.g.f.: (1+(x+1)*sinh(x))/(1-x).

a(n) = A155521(n-1) + A344262(n) for n > 0.

Lim_{n->infinity} a(n)/n! = 1+2*sinh(1) = 1+e-1/e = 1+A174548. - Amrit Awasthi, May 19 2021