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%I #2 Mar 30 2012 18:37:15
%S 1,2,2,16,6,3,230,54,12,4,4704,818,128,20,5,124388,17360,2162,250,30,
%T 6,4029888,472484,49600,4742,432,42,7,154462924,15666720,1432844,
%U 118920,9158,686,56,8,6834212520,612024124,49817952,3688268,251216,16130,1024
%N Triangle, read by rows, where T(n,k) = Sum_{i=k..n-1} T(n-1,i)*T(i+1,k+1) for n>k with T(n,n) = n+1 for n>=0.
%e Triangle begins:
%e 1;
%e 2, 2;
%e 16, 6, 3;
%e 230, 54, 12, 4;
%e 4704, 818, 128, 20, 5;
%e 124388, 17360, 2162, 250, 30, 6;
%e 4029888, 472484, 49600, 4742, 432, 42, 7;
%e 154462924, 15666720, 1432844, 118920, 9158, 686, 56, 8;
%e 6834212520, 612024124, 49817952, 3688268, 251216, 16130, 1024, 72, 9;
%e 342732052968, 27510397296, 2023012156, 135928128, 8390756, 482464, 26498, 1458, 90, 10;
%e ...
%e Illustrate the recurrence by row and column vector products:
%e T(3,0) = [16,6,3] * [2,6,54]~ = 16*2 + 6*6 + 3*54 = 230;
%e T(4,1) = [54,12,4] * [3,12,128]~ = 818;
%e T(4,0) = [230,54,12,4] * [2,6,54,818]~ = 4704.
%o (PARI) {T(n,k)=if(n==k,n+1,sum(i=k,n-1,T(n-1,i)*T(i+1,k+1)))}
%Y Cf. A152542, A152543, A152544.
%K nonn,tabl
%O 0,2
%A _Paul D. Hanna_, Dec 12 2008
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