OFFSET
0,5
LINKS
Eric Weisstein's World of Mathematics, Laguerre Polynomial
Wikipedia, Laguerre polynomials
FORMULA
T(n,k) = Sum_{j=0..n} (k*n)^j * (n-j)! * binomial(n,j)^2.
T(n,k) = n! * [x^n] exp(k*n*x/(1-x))/(1-x).
T(n,k) = A289192(n,k*n).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, ...
2, 14, 34, 62, 98, ...
6, 168, 654, 1626, 3246, ...
24, 2840, 17688, 59928, 151064, ...
MATHEMATICA
T[n_, k_] := n! * LaguerreL[n, -k*n]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* Amiram Eldar, Feb 05 2021 *)
PROG
(PARI) T(n, k) = sum(j=0, n, (k*n)^j*(n-j)!*binomial(n, j)^2);
(PARI) T(n, k) = n!*pollaguerre(n, 0, -k*n); \\ Michel Marcus, Feb 05 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Feb 05 2021
STATUS
approved