This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A344419 #18 May 21 2021 18:17:48
%S A344419 0,1,3,12,49,250,1501,10514,84113,757026,7570261,83272882,999274585,
%T A344419 12990569618,181867974653,2728019619810,43648313916961,
%U A344419 742021336588354,13356384058590373,253771297113217106,5075425942264342121,106583944787551184562,2344846785326126060365
%N A344419 a(n) = n*a(n-1) + n^(n mod 2), a(0) = 0.
%H A344419 Alois P. Heinz, <a href="/A344419/b344419.txt">Table of n, a(n) for n = 0..450</a>
%F A344419 E.g.f.: ((x+1)*cosh(x)-1)/(1-x).
%F A344419 a(n) = A344262(n) - n! = A344262(n) - A000142(n).
%F A344419 a(n) = A344418(n) - A155521(n-1) for n > 0.
%F A344419 Lim_{n->infinity} a(n)/n! = 2*cosh(1)-1 = 2*A073743-1 = e+1/e-1 = A137204-1. - _Amrit Awasthi_, May 20 2021
%p A344419 a:= proc(n) a(n):= n*a(n-1) + n^(n mod 2) end: a(0):= 0:
%p A344419 seq(a(n), n=0..23);
%Y A344419 Cf. A000142, A001113, A073743, A155521, A137204, A344262, A344418.
%K A344419 nonn
%O A344419 0,3
%A A344419 _Alois P. Heinz_, May 17 2021