OFFSET
0,2
FORMULA
T(n,k) = binomial(n+1,n-k)^2*binomial(2*k,k)/(k+1). - Detlef Meya, Nov 19 2023
EXAMPLE
Triangle T(n, k) starts:
[0] 1;
[1] 4, 1;
[2] 9, 9, 2;
[3] 16, 36, 32, 5;
[4] 25, 100, 200, 125, 14;
[5] 36, 225, 800, 1125, 504, 42;
[6] 49, 441, 2450, 6125, 6174, 2058, 132;
[7] 64, 784, 6272, 24500, 43904, 32928, 8448, 429;
[8] 81, 1296, 14112, 79380, 222264, 296352, 171072, 34749, 1430;
[9] 100, 2025, 28800, 220500, 889056, 1852200, 1900800, 868725, 143000, 4862;
MAPLE
p := n -> (1 - hypergeom([-1/2, -n-1, -n-1], [1, 1], 4*x)) / (2*x):
T := (n, k) -> coeff(simplify(p(n)), x, k):
seq(seq(T(n, k), k = 0..n), n = 0..9);
MATHEMATICA
T[n_, k_]:=Binomial[n+1, n-k]^2*Binomial[2*k, k]/(k+1); Flatten[Table[T[n, k], {n, 0, 9}, {k, 0, n}]] (* Detlef Meya, Nov 19 2023 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Nov 07 2023
STATUS
approved