A344418 - OEIS

%I #20 May 21 2021 18:16:29

%S 0,1,4,13,56,281,1692,11845,94768,852913,8529140,93820541,1125846504,

%T 14636004553,204904063756,3073560956341,49176975301472,

%U 836008580125025,15048154442250468,285914934402758893,5718298688055177880,120084272449158735481,2641853993881492180604

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

%H Alois P. Heinz, <a href="/A344418/b344418.txt">Table of n, a(n) for n = 0..450</a>

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

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

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

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

%p a:= proc(n) a(n):= n*a(n-1) + n^(1+n mod 2) end: a(0):= 0:

%p seq(a(n), n=0..23);

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

%K nonn

%O 0,3

%A _Alois P. Heinz_, May 17 2021