OFFSET
0,3
FORMULA
G.f. of column k: 1/sqrt(1 - 4*x*(1-x)^k).
n*T(n,k) = 2 * Sum_{j=0..k} (-1)^j * binomial(k,j)*(2*n-1-j)*T(n-1-j,k) for n > k.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, 2, 2, ...
6, 4, 2, 0, -2, -4, -6, ...
20, 8, -2, -10, -16, -20, -22, ...
70, 16, -14, -22, -10, 20, 66, ...
252, 32, -32, 12, 118, 242, 342, ...
924, 64, -30, 174, 304, 82, -678, ...
PROG
(PARI) T(n, k) = sum(j=0, n, (-1)^(n-j)*binomial(2*j, j)*binomial(k*j, n-j));
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Mar 26 2023
STATUS
approved