OFFSET
0,9
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
T(0,k) = 1 and T(n,k) = -(n-1)! * Sum_{j=k+1..n} (-1)^(j-k) * j/(j-k) * T(n-j,k)/(n-j)! for n > 0.
T(n,k) = n! * Sum_{j=0..floor(n/(k+1))} Stirling1(n-k*j,j)/(n-k*j)!.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 0, 0, 0, 0, 0, 0, ...
0, 2, 0, 0, 0, 0, 0, ...
0, -3, 6, 0, 0, 0, 0, ...
0, 20, -12, 24, 0, 0, 0, ...
0, -90, 40, -60, 120, 0, 0, ...
0, 594, 180, 240, -360, 720, 0, ...
PROG
(PARI) T(n, k) = n!*sum(j=0, n\(k+1), stirling(n-k*j, j, 1)/(n-k*j)!);
CROSSREFS
AUTHOR
Seiichi Manyama, Jul 09 2022
STATUS
approved