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 A224869 #23 Dec 02 2024 16:53:54
%S A224869 -1,0,3,16,85,516,3619,28960,260649,2606500,28671511,344058144,
%T A224869 4472755885,62618582404,939278736075,15028459777216,255483816212689,
%U A224869 4598708691828420,87375465144739999,1747509302894800000,36697695360790800021,807349297937397600484
%N A224869 a(n) = n*( a(n-1)+1 ), initialized by a(1) = -1.
%F A224869 a(n) +(-n-2)*a(n-1) +(2*n-1)*a(n-2) +(-n+2)*a(n-3)=0. - _R. J. Mathar_, Jul 28 2013
%F A224869 a(n) = exp(1)*n*Gamma(n,1) - 2*Gamma(n+1,0). - _Martin Clever_, Mar 27 2023
%e A224869 a(4) = 4*(a(3)+1) = 4*4 = 16.
%t A224869 A224869[1] := -1; A224869[n_] := A224869[n - 1]n + n; Table[A224869[n], {n, 40}] (* _Alonso del Arte_, Jul 22 2013 *)
%o A224869 (Python)
%o A224869 a=-1
%o A224869 for n in range(2,24):
%o A224869 print(a, end=', ')
%o A224869 a= n*(a+1)
%Y A224869 Cf. A007526, A038156, A166554, A121662 (3rd column).
%K A224869 sign,easy
%O A224869 1,3
%A A224869 _Alex Ratushnyak_, Jul 22 2013