OFFSET
0,3
FORMULA
T(n, k) = binomial(n, k)^2 * binomial(2*k, k).
EXAMPLE
Triangle T(n, k) starts:
[0] 1;
[1] 1, 2;
[2] 1, 8, 6;
[3] 1, 18, 54, 20;
[4] 1, 32, 216, 320, 70;
[5] 1, 50, 600, 2000, 1750, 252;
[6] 1, 72, 1350, 8000, 15750, 9072, 924;
[7] 1, 98, 2646, 24500, 85750, 111132, 45276, 3432;
[8] 1, 128, 4704, 62720, 343000, 790272, 724416, 219648, 12870;
[9] 1, 162, 7776, 141120, 1111320, 4000752, 6519744, 4447872, 1042470, 48620;
MAPLE
p := n -> hypergeom([1/2, -n, -n], [1, 1], 4*x):
T := (n, k) -> coeff(simplify(p(n)), x, k):
seq(seq(T(n, k), k = 0..n), n = 0..9);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Nov 07 2023
STATUS
approved