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 A109450 #8 Sep 08 2013 13:30:45 %S A109450 1,0,1,0,1,2,0,1,5,5,0,1,8,20,14,0,1,11,44,75,42,0,1,14,77,208,275, %T A109450 132,0,1,17,119,440,910,1001,429,0,1,20,170,798,2244,3808,3640,1430,0, %U A109450 1,23,230,1309,4655,10659,15504,13260,4862,0,1,26,299,2000 %N A109450 Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is the operator defined in A084938. %C A109450 Row sums : 1, 1, 3, 11, 43, 173, .... (see A026671). %C A109450 Transposed version in A107842. %F A109450 T(0, 0) = 1, T(n, 0) = 0 if n>0, T(n, k) = 0 if k>n, T(n, k) = (3n-3k+2)*binomial(3n-k-1, k-1)/(3n-2k+1). %F A109450 T(n, n) = A000108(n), Catalan numbers. %e A109450 Triangle begins: %e A109450 1; %e A109450 0, 1; %e A109450 0, 1, 2; %e A109450 0, 1, 5, 5; %e A109450 0, 1, 8, 20, 14; %e A109450 0, 1, 11, 44, 75, 42; %e A109450 0, 1, 14, 77, 208, 275, 132 %Y A109450 Cf. A000108, A000344, A003518, A000589, A107842. %K A109450 easy,nonn,tabl %O A109450 0,6 %A A109450 _Philippe Deléham_, Aug 26 2005