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 A202992 #9 Feb 22 2013 14:40:24
%S A202992 1,1,0,2,0,0,5,1,0,0,14,8,2,0,0,42,46,26,6,0,0,132,232,220,112,24,0,0,
%T A202992 429,1093,1527,1275,596,120,0,0,1430,4944,9436,11384,8638,3768,720,0,
%U A202992 0,4862,21778,54004,87556,95126,66938,27576,5040,0,0
%N A202992 Triangle T(n,k), read by rows, given by (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...) DELTA (0, 0, 1, 1, 2, 2, 3, 3, 4, 4, ...) where DELTA is the operator defined in A084938.
%C A202992 T(n,0) = A000108(n) (the Catalan numbers).
%C A202992 Row sums are the factorials (A000142).
%F A202992 T(n,0) = A000108(n), Catalan numbers. Row sums = n! = A000142(n).
%F A202992 T(n+2,n) = n!, n>0.
%F A202992 Sum_{k, 0<=k<=n} T(n,k)*x^k = A011782(n), A000108(n), A000142(n) for x = -1, 0, 1 respectively.
%e A202992 Triangle begins :
%e A202992 1
%e A202992 1, 0
%e A202992 2, 0, 0
%e A202992 5, 1, 0, 0
%e A202992 14, 8, 2, 0, 0
%e A202992 42, 46, 26, 6, 0, 0
%e A202992 132, 232, 220, 112, 24, 0, 0
%Y A202992 Cf. A000108, A000142, A011782, A145879
%K A202992 nonn,tabl
%O A202992 0,4
%A A202992 _Philippe Deléham_, Dec 26 2011