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 A188587 #12 Feb 03 2019 01:28:25 %S A188587 1,1,1,1,1,1,1,5,5,1,1,14,30,14,1,1,33,146,146,33,1,1,72,603,1168,603, %T A188587 72,1,1,151,2241,7687,7687,2241,151,1,1,310,7780,44194,76870,44194, %U A188587 7780,310,1,1,629,25820,231236,649514,649514,231236,25820,629,1,1,1268,83121,1131504,4866222,7794168,4866222,1131504,83121,1268,1 %N A188587 1-Euler triangle. %C A188587 Formed with the same recurrence as the Euler triangle A008292 (adjusted for offset), but with the middle element of row n=2 set to 1. %C A188587 Row sums are A188588. Second column is A188589. %F A188587 T(n,k) = 0 if k < 0 or k > n. %F A188587 T(n,k) = 1 if k=0 or k=n or n=2. %F A188587 T(n,k)= (n-k+1)*T(n-1,k-1) + (k+1)*T(n-1,k), n > 2 and 1 <= k < n. %e A188587 Triangle begins %e A188587 1; %e A188587 1, 1; %e A188587 1, 1, 1; %e A188587 1, 5, 5, 1; %e A188587 1, 14, 30, 14, 1; %e A188587 1, 33, 146, 146, 33, 1; %e A188587 1, 72, 603, 1168, 603, 72, 1; %e A188587 1, 151, 2241, 7687, 7687, 2241, 151, 1; %e A188587 1, 310, 7780, 44194, 76870, 44194, 7780, 310, 1; %e A188587 1, 629, 25820, 231236, 649514, 649514, 231236, 25820, 629, 1; %p A188587 A188587 := proc(n,k) if k < 0 or k > n then 0; elif k=0 or k= n or n=2 then 1; else (n-k+1)*procname(n-1,k-1)+(k+1)*procname(n-1,k) ; end if; end proc: %p A188587 seq(seq(A188587(n,k),k=0..n),n=0..10) ; # _R. J. Mathar_, Apr 13 2011 %K A188587 nonn,easy,tabl %O A188587 0,8 %A A188587 _Paul Barry_, Apr 04 2011