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 A072374 #15 Feb 11 2014 05:08:08
%S A072374 1,2,3,6,11,24,51,122,291,756,1979,5526,15627,46496,140451,442194,
%T A072374 1414931,4687212,15785451,54764846,193129659,698978136,2570480147,
%U A072374 9672977706,36967490691,144232455524,571177352091,2304843053382,9434493132011,39289892366736
%N A072374 a(1) = 1; a(n) = 1 + Sum_{i=1..n} Product_{j=i..2*i-1} (n-j).
%C A072374 A122852 is another version of the same sequence. - _R. J. Mathar_, Jun 18 2008
%H A072374 Vincenzo Librandi, <a href="/A072374/b072374.txt">Table of n, a(n) for n = 1..200</a>
%F A072374 The sequence 1, 1, 2, 3, .. has a(n)=sum{k=0..floor(n/2), C(n-k, k)k!} (diagonal sums of permutation triangle A008279). - _Paul Barry_, May 12 2004
%F A072374 Recurrence: 2*a(n) = 3*a(n-1) + (n-1)*a(n-2) - (n-1)*a(n-3). - _Vaclav Kotesovec_, Feb 08 2014
%F A072374 a(n) ~ sqrt(Pi) * exp(sqrt(n/2) - n/2 + 1/8) * n^((n+1)/2) / 2^(n/2+1) * (1 + 37/(48*sqrt(2*n))). - _Vaclav Kotesovec_, Feb 08 2014
%t A072374 Table[Sum[Binomial[n-k,k]*k!,{k,0,Floor[n/2]}],{n,1,20}] (* _Vaclav Kotesovec_, Feb 08 2014 *)
%K A072374 nonn
%O A072374 1,2
%A A072374 _N. J. A. Sloane_, Jul 19 2002