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 A112369 #14 May 09 2024 14:31:58
%S A112369 0,2,10,58,442,4282,50362,695482,11017402,196811962,3912703162,
%T A112369 85662309562,2047652863162,53059407256762,1481388530277562,
%U A112369 44331262220901562,1415527220320869562,48036189795719781562,1726380042510080613562,65503446445655792229562,2616586102571484256869562
%N A112369 a(n) = -1 + Sum_{i=0..n} 2^i*i!.
%t A112369 s = 0; lst = {s}; Do[s += n!!; AppendTo[lst, s], {n, 2, 38, 2}]; lst (* _Zerinvary Lajos_, Jul 13 2009 *)
%t A112369 Join[{0},Accumulate[Table[2^x x!,{x,20}]]] (* _Harvey P. Dale_, Apr 01 2018 *)
%Y A112369 Cf. A004400, A112368.
%K A112369 nonn
%O A112369 0,2
%A A112369 _N. J. A. Sloane_, Dec 02 2005