OFFSET
0,8
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
A(0,k) = 1 and A(n,k) = k * (n-1)! * Sum_{j=1..n} binomial(j+k-1,k)*A(n-j,k)/(n-j)! for n > 0.
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, ...
0, 3, 10, 21, 36, ...
0, 13, 68, 195, 424, ...
0, 73, 580, 2241, 6136, ...
0, 501, 5912, 30483, 104544, ...
MATHEMATICA
A[0, _] = 1; A[n_, k_] := k*(n-1)!*Sum[Binomial[j+k-1, k]*A[n-j, k]/(n-j)!, {j, 1, n}];
Table[A[n-k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Nov 03 2017 *)
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Oct 22 2017
STATUS
approved