OFFSET
0,2
LINKS
FORMULA
EXAMPLE
The triangle begins:
1;
2, -1;
12, -8, 1;
120, -90, 18, -1;
1680, -1344, 336, -32, 1;
30240, -25200, 7200, -900, 50, -1;
665280, -570240, 178200, -26400, 1980, -72, 1;
MATHEMATICA
T[n_, k_] := (-1)^k * (2*n)! * Binomial[n, k]/(k + n)!; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, May 11 2021 *)
PROG
(PARI) T(n, k) = (-1)^k*(2*n)!*binomial(n, k)/(k+n)!;
(PARI) row(n) = Vecrev(n!*pollaguerre(n, n));
(Magma) [(-1)^k*Factorial(n-k)*Binomial(n, k)*Binomial(2*n, n+k): k in [0..n], n in [0..12]]; // G. C. Greubel, Aug 11 2022
(SageMath)
def A343861(n, k): return (-1)^k*factorial(n-k)*binomial(n, k)*binomial(2*n, n+k)
flatten([[A343861(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Aug 11 2022
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, May 01 2021
STATUS
approved