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 A344317 #28 May 19 2021 03:25:14
%S A344317 1,2,6,19,80,401,2412,16885,135088,1215793,12157940,133737341,
%T A344317 1604848104,20863025353,292082354956,4381235324341,70099765189472,
%U A344317 1191696008221025,21450528147978468,407560034811590893,8151200696231817880,171175214620868175481
%N A344317 a(n) = n*a(n-1) + n^(1+n mod 2), a(0) = 1.
%H A344317 Alois P. Heinz, <a href="/A344317/b344317.txt">Table of n, a(n) for n = 0..450</a>
%F A344317 E.g.f.: (1+(x+1)*sinh(x))/(1-x).
%F A344317 a(n) = A155521(n-1) + A344262(n) for n > 0.
%F A344317 Lim_{n->infinity} a(n)/n! = 1+2*sinh(1) = 1+e-1/e = 1+A174548. - _Amrit Awasthi_, May 19 2021
%p A344317 a:= proc(n) a(n):= n*a(n-1) + n^(1+n mod 2) end: a(0):= 1:
%p A344317 seq(a(n), n=0..23);
%Y A344317 Cf. A155521, A174548, A344229, A344262.
%K A344317 nonn
%O A344317 0,2
%A A344317 _Alois P. Heinz_, May 14 2021