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 A344418 #20 May 21 2021 18:16:29
%S A344418 0,1,4,13,56,281,1692,11845,94768,852913,8529140,93820541,1125846504,
%T A344418 14636004553,204904063756,3073560956341,49176975301472,
%U A344418 836008580125025,15048154442250468,285914934402758893,5718298688055177880,120084272449158735481,2641853993881492180604
%N A344418 a(n) = n*a(n-1) + n^(1+n mod 2), a(0) = 0.
%H A344418 Alois P. Heinz, <a href="/A344418/b344418.txt">Table of n, a(n) for n = 0..450</a>
%F A344418 E.g.f.: (x+1)*sinh(x)/(1-x).
%F A344418 a(n) = A344317(n) - n! = A344317(n) - A000142(n).
%F A344418 a(n) = A155521(n-1) + A344419(n) for n > 0.
%F A344418 Lim_{n-> infinity} a(n)/n! = 2*sinh(1) = 2*A073742 = e-1/e = A174548. - _Amrit Awasthi_, May 20 2021
%p A344418 a:= proc(n) a(n):= n*a(n-1) + n^(1+n mod 2) end: a(0):= 0:
%p A344418 seq(a(n), n=0..23);
%Y A344418 Cf. A000142, A001113, A073742, A155521, A174548, A344317, A344419.
%K A344418 nonn
%O A344418 0,3
%A A344418 _Alois P. Heinz_, May 17 2021