OFFSET
0,12
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
T(0,k) = 1 and T(n,k) = T(n-1,k) - k * Sum_{j=0..n-1} binomial(n-1,j) * T(j,k) for n > 0.
T(n,k) = exp(k) * Sum_{j>=0} (j + 1)^n * (-k)^j / j!.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 0, -1, -2, -3, -4, -5, ...
1, -1, -1, 1, 5, 11, 19, ...
1, -1, 3, 7, 5, -9, -41, ...
1, 2, 7, -8, -43, -74, -53, ...
1, 9, -13, -65, -27, 221, 679, ...
1, 9, -89, 37, 597, 961, -341, ...
MATHEMATICA
T[0, k_] := 1; T[n_, k_] := T[n - 1, k] - k * Sum[T[j, k] * Binomial[n - 1, j], {j, 0, n - 1}]; Table[T[n - k, k], {n, 0, 11}, {k, n, 0, -1}] // Flatten (* Amiram Eldar, Jul 03 2020 *)
CROSSREFS
AUTHOR
Seiichi Manyama, Jul 03 2020
STATUS
approved