OFFSET
0,4
COMMENTS
Column 0 of matrix square T^2 equals column 0 of T shift left. Central terms are T(2*n,n) = (n+1)*A125279(n).
FORMULA
EXAMPLE
Triangle begins:
1;
1, 1;
2, 2, 1;
6, 5, 3, 1;
23, 16, 9, 4, 1;
104, 62, 31, 14, 5, 1;
531, 278, 123, 52, 20, 6, 1;
2982, 1398, 552, 213, 80, 27, 7, 1;
18109, 7718, 2750, 964, 340, 116, 35, 8, 1;
117545, 46083, 14976, 4784, 1561, 513, 161, 44, 9, 1;
808764, 294392, 88083, 25792, 7755, 2400, 742, 216, 54, 10, 1; ...
Matrix square T^2 begins:
1;
2, 1;
6, 4, 1;
23, 16, 6, 1;
104, 70, 30, 8, 1;
531, 336, 149, 48, 10, 1; ...
which is also a convolution triangle.
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(n==k, 1, if(k>0, sum(j=0, n-k, T(j, 0)*T(n-1-j, k-1)), sum(j=0, n-1, T(j, 0)*T(n-1, j)))))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 26 2006
STATUS
approved