OFFSET
0,9
LINKS
Seiichi Manyama, Antidiagonals n = 0..55, flattened
FORMULA
G.f. A_k(x) of column k satisfies A_k(x) = 1 + x * A_k(k * x / (1 - x)) / (1 - x). - Seiichi Manyama, Jun 18 2022
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, ...
1, 5, 17, 43, 89, 161, ...
1, 15, 179, 1279, 5949, 20591, ...
1, 52, 3489, 108472, 1546225, 12950796, ...
MAPLE
A:= proc(n, k) option remember; `if`(n=0, 1,
add(k^j*binomial(n-1, j)*A(j, k), j=0..n-1))
end:
seq(seq(A(n, d-n), n=0..d), d=0..12); # Alois P. Heinz, Jul 28 2019
MATHEMATICA
A[0, _] = 1;
A[n_, k_] := A[n, k] = Sum[k^j Binomial[n-1, j] A[j, k], {j, 0, n-1}];
Table[A[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, May 29 2020 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jul 28 2019
STATUS
approved