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 A238763 #10 Mar 15 2014 15:24:57
%S A238763 1,0,1,1,0,2,0,2,0,4,1,0,5,0,9,0,3,0,12,0,21,1,0,9,0,30,0,51,0,4,0,25,
%T A238763 0,76,0,127,1,0,14,0,69,0,196,0,323,0,5,0,44,0,189,0,512,0,835,1,0,20,
%U A238763 0,133,0,518,0,1353,0,2188,0,6,0,70,0,392,0,1422,0
%N A238763 A Motzkin triangle read by rows, 0<=k<=n.
%C A238763 Similar to A020474 but with a different enumeration.
%C A238763 Compare with the definition of the generalized ballot numbers A238762.
%F A238763 Definition: T(0, 0) = 1; T(p, q) = 0 if p < 0 or p > q; T(p, q) = T(p-2, q) + T(p-1, q-1) + T(p, q-2). (The notation is in the style of Knuth, TAOCP 4a (7.2.1.6)).
%F A238763 T(n, n) = A001006(n).
%F A238763 Sum_{0<=k<=n} T(n, k) = A005043(n+2).
%e A238763 [n\k 0 1 2 3 4 5 6 7]
%e A238763 [0] 1,
%e A238763 [1] 0, 1,
%e A238763 [2] 1, 0, 2,
%e A238763 [3] 0, 2, 0, 4,
%e A238763 [4] 1, 0, 5, 0, 9,
%e A238763 [5] 0, 3, 0, 12, 0, 21,
%e A238763 [6] 1, 0, 9, 0, 30, 0, 51,
%e A238763 [7] 0, 4, 0, 25, 0, 76, 0, 127.
%o A238763 (Sage)
%o A238763 @CachedFunction
%o A238763 def T(p, q):
%o A238763 if p == 0 and q == 0: return 1
%o A238763 if p < 0 or p > q: return 0
%o A238763 return T(p-2, q) + T(p-1, q-1) + T(p, q-2)
%o A238763 [[T(p, q) for p in (0..q)] for q in (0..9)]
%Y A238763 Cf. A001006, A005043, A064189, A020474, A238762.
%K A238763 nonn,tabl
%O A238763 0,6
%A A238763 _Peter Luschny_, Mar 05 2014