OFFSET
0,8
LINKS
Alois P. Heinz, Antidiagonals n = 0..24, flattened
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 2, 6, 24, 120, ...
1, 2, 16, 288, 9216, 460800, ...
1, 5, 192, 24444, 7303104, 4234233600, ...
1, 14, 2816, 2738592, 8204167296, 59027412643200, ...
1, 42, 46592, 361998432, 11332298092032, 1052109889288796160, ...
MAPLE
b:= proc(n, l) option remember; `if`(n=0, 1, (k-> add(
`if`(l[i]>0, b(n-1, sort(subsop(i=l[i]-1, l))), 0), i=1..k)+
`if`(add(i, i=l)+k<n, b(n-1, map(x-> x+1, l)), 0))(nops(l)))
end:
A:= (n, k)-> b(k*n+n, [0$k]):
seq(seq(A(n, d-n), n=0..d), d=0..10);
MATHEMATICA
b[n_, l_] := b[n, l] = If[n == 0, 1, Function[k, Sum[
If[l[[i]]>0, b[n-1, Sort[ReplacePart[l, i -> l[[i]]-1]]], 0], {i, 1, k}]+
If[Sum[i, {i, l}] + k < n, b[n - 1, Map[#+1&, l]], 0]][Length[l]]];
A[n_, k_] := b[k*n + n, Table[0, {k}]];
Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 10}] // Flatten (* Jean-François Alcover, Jan 26 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
AUTHOR
Alois P. Heinz, Jan 12 2021
STATUS
approved