OFFSET
0,9
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(k,n)} j*A(n-j,k)/(n-j)!.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
1, 3, 3, 3, 3, ...
1, 7, 13, 13, 13, ...
1, 25, 49, 73, 73, ...
1, 81, 261, 381, 501, ...
MAPLE
A:= proc(n, k) option remember; `if`(n=0, 1, add(
A(n-j, k)*binomial(n-1, j-1)*j!, j=1..min(n, k)))
end:
seq(seq(A(n, 1+d-n), n=0..d), d=0..12); # Alois P. Heinz, Nov 11 2020
MATHEMATICA
A[0, _] = 1; A[n_ /; n >= 0, k_ /; k >= 1] := A[n, k] = (n-1)!*Sum[j*A[n-j, k]/(n-j)!, {j, 1, Min[k, n]}]; A[_, _] = 0;
Table[A[n, d-n+1], {d, 0, 12}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 13 2021 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Oct 14 2017
STATUS
approved