A344419 a(n) = n*a(n-1) + n^(n mod 2), a(0) = 0.

0, 1, 3, 12, 49, 250, 1501, 10514, 84113, 757026, 7570261, 83272882, 999274585, 12990569618, 181867974653, 2728019619810, 43648313916961, 742021336588354, 13356384058590373, 253771297113217106, 5075425942264342121, 106583944787551184562, 2344846785326126060365

Offset

0,3

Links

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

Formula

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

a(n) = A344262(n) - n! = A344262(n) - A000142(n).

a(n) = A344418(n) - A155521(n-1) for n > 0.

Lim_{n->infinity} a(n)/n! = 2*cosh(1)-1 = 2*A073743-1 = e+1/e-1 = A137204-1. - Amrit Awasthi, May 20 2021

Maple

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

Crossrefs

Cf. A000142, A001113, A073743, A155521, A137204, A344262, A344418.

Sequence in context: A151175 A151176 A151177 * A002179 A224659 A034541

Adjacent sequences: A344416 A344417 A344418 * A344420 A344421 A344422

Keyword

nonn

Author

Alois P. Heinz, May 17 2021

Status

approved