A344418 a(n) = n*a(n-1) + n^(1+n mod 2), a(0) = 0.

0, 1, 4, 13, 56, 281, 1692, 11845, 94768, 852913, 8529140, 93820541, 1125846504, 14636004553, 204904063756, 3073560956341, 49176975301472, 836008580125025, 15048154442250468, 285914934402758893, 5718298688055177880, 120084272449158735481, 2641853993881492180604

Offset: 0

Author

Alois P. Heinz, May 17 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A000142, A001113, A073742, A155521, A174548, A344317, A344419.

Programs

Maple

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

Formula

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

a(n) = A344317(n) - n! = A344317(n) - A000142(n).

a(n) = A155521(n-1) + A344419(n) for n > 0.

Lim_{n-> infinity} a(n)/n! = 2*sinh(1) = 2*A073742 = e-1/e = A174548. - Amrit Awasthi, May 20 2021