OFFSET
0,5
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
E.g.f. of column k: exp(x/(1-k*x)) / (1-k*x).
T(n,k) = (2*k*n-k+1) * T(n-1,k) - k^2 * (n-1)^2 * T(n-2,k) for n > 1.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, ...
1, 7, 17, 31, 49, 71, ...
1, 34, 139, 352, 709, 1246, ...
1, 209, 1473, 5233, 13505, 28881, ...
1, 1546, 19091, 95836, 318181, 830126, ...
MATHEMATICA
T[n_, k_] := Sum[If[j == k == 0, 1, k^j]*j!*Binomial[n, j]^2, {j, 0, n}]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* Amiram Eldar, Feb 02 2021 *)
PROG
(PARI) {T(n, k) = sum(j=0, n, k^j*j!*binomial(n, j)^2)}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Feb 02 2021
STATUS
approved