OFFSET
0,5
LINKS
D. Gouyou-Beauchamps, Chemins sous-diagonaux et tableau de Young, pp. 112-125 of "Combinatoire Enumérative (Montreal 1985)", Lect. Notes Math. 1234, 1986.
FORMULA
T(n, k) = (n+k)!*(n+k+2)!*(n-k+3)!/(k!*(k+1)!*(n-k)!*(n+2)!*(n+3)!) for 0 <= k <= n. - Emeric Deutsch, Apr 29 2004
EXAMPLE
Triangle begins
1;
1, 1;
1, 3, 3;
1, 6, 14, 14;
...
MAPLE
T:=(n, k)->(n+k)!*(n+k+2)!*(n-k+3)!/k!/(k+1)!/(n-k)!/(n+2)!/(n+3)!: seq(seq(T(n, k), k=0..n), n=0..10);
MATHEMATICA
Flatten[Table[(n+k)!(n+k+2)!(n-k+3)!/(k!(k+1)!(n-k)!(n+2)!(n+3)!), {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Jul 16 2012 *)
PROG
(PARI) T(n, k)=(n+k)!*(n+k+2)!*(n-k+3)!/(k!*(k+1)!*(n-k)!*(n+2)!*(n+3)!);
matrix(10, 10, n, k, if (n>=k, T(n-1, k-1))) \\ Michel Marcus, Mar 05 2020
(Magma) /* As triangle */ [[Factorial(n + k) * Factorial(n + k + 2) * Factorial(n - k + 3) / (Factorial(k) * Factorial(k + 1) * Factorial(n - k) * Factorial(n + 2) * Factorial(n + 3)): k in [0..n]]: n in [0.. 10]]; // Vincenzo Librandi, Mar 06 2020
CROSSREFS
KEYWORD
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch, Apr 29 2004
STATUS
approved