OFFSET
0,9
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, ...
0, 2, 3, 3, 3, ...
0, 12, 12, 13, 13, ...
0, 48, 72, 72, 73, ...
0, 360, 480, 500, 500, ...
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1, k)/j!, j=0..min(k, n/i))))
end:
A:= (n, k)-> n!*b(n$2, k):
seq(seq(A(n, d-n), n=0..d), d=0..12); # Alois P. Heinz, Oct 02 2017
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i j, i - 1, k]/j!, {j, 0, Min[k, n/i]}]]];
A[n_, k_] := n! b[n, n, k];
Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Dec 06 2019, after Alois P. Heinz *)
CROSSREFS
AUTHOR
Seiichi Manyama, Oct 01 2017
STATUS
approved