OFFSET
0,2
LINKS
FORMULA
T(n, k) = (-1)^k * n! * binomial(2*n+1,n-k)/k! = (-1)^k * (2*n+1)! * binomial(n,k)/(k+n+1)!.
EXAMPLE
The triangle begins:
1;
3, -1;
20, -10, 1;
210, -126, 21, -1;
3024, -2016, 432, -36, 1;
55440, -39600, 9900, -1100, 55, -1;
1235520, -926640, 257400, -34320, 2340, -78, 1;
MATHEMATICA
T[n_, k_] := (-1)^k * (2*n + 1)! * Binomial[n, k]/(k + n + 1)!; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, May 03 2021 *)
PROG
(PARI) T(n, k) = (-1)^k*(2*n+1)!*binomial(n, k)/(k+n+1)!;
(PARI) row(n) = Vecrev(n!*pollaguerre(n, n+1));
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, May 03 2021
STATUS
approved