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EXAMPLE
| Other recurrences exist, as shown by:
column 0 = A000698: T(n,0) = (2n+1)!! - Sum_{k=1..n} (2k-1)!!*T(n-k,0);
column 1 = A115974: T(n,1) = T(n+1,0) - Sum_{k=0..n-1} T(k,1)*T(n-k,0).
Illustrate the recurrence:
T(n,k) = Sum_{j=0..n-k-1) T(j+k,k)*T(n-j,k+1) (n>k>=0)
at column k=1:
T(2,1) = T(1,1)*T(2,2) = 2*3 = 6;
T(3,1) = T(1,1)*T(3,2) + T(2,1)*T(2,2) = 2*12 + 6*3 = 42;
T(4,1) = T(1,1)*T(4,2) + T(2,1)*T(3,2) + T(3,1)*T(2,2) = 2*108 + 6*12 + 42*3 = 414;
at column k=2:
T(3,2) = T(2,2)*T(3,3) = 3*4 = 12;
T(4,2) = T(2,2)*T(4,3) + T(3,2)*T(3,3) = 3*20 + 12*4 = 108;
T(5,2) = T(2,2)*T(5,3) + T(3,2)*T(4,3) + T(4,2)*T(3,3) = 3*220 + 12*20 + 108*4 = 1332.
Triangle begins:
1;
2, 2;
10, 6, 3;
74, 42, 12, 4;
706, 414, 108, 20, 5;
8162, 5058, 1332, 220, 30, 6;
110410, 72486, 19908, 3260, 390, 42, 7;
1708394, 1182762, 342252, 57700, 6750, 630, 56, 8;
29752066, 21573054, 6583788, 1159700, 138150, 12474, 952, 72, 9; ...
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