OFFSET
0,13
LINKS
Alois P. Heinz, Antidiagonals n = 0..43, flattened
EXAMPLE
A(2,3) = 3: (1,1), (1,2), (1,3).
A(3,2) = 7: (1,1,1), (1,1,2), (1,1,3), (1,1,4), (1,2,2), (1,2,3), (1,2,4).
A(3,3) = 24: (1,1,1), (1,1,2), (1,1,3), (1,1,4), (1,1,5), (1,1,6), (1,1,7), (1,1,8), (1,1,9), (1,2,2), (1,2,3), (1,2,4), (1,2,5), (1,2,6), (1,2,7), (1,2,8), (1,2,9), (1,3,3), (1,3,4), (1,3,5), (1,3,6), (1,3,7), (1,3,8), (1,3,9).
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 1, 7, 24, 58, 115, 201, ...
0, 1, 44, 541, 3236, 12885, 39656, ...
0, 1, 516, 35649, 713727, 7173370, 46769781, ...
0, 1, 11622, 6979689, 627642640, 19940684251, 330736663032, ...
MAPLE
A:= proc(n, k) option remember; `if`(n=0, 1, -add(
A(j, k)*(-1)^(n-j)*binomial(k^j, n-j), j=0..n-1))
end:
seq(seq(A(n, d-n), n=0..d), d=0..12);
MATHEMATICA
A[n_, k_] := A[n, k] = If[n==0, 1, -Sum[A[j, k]*(-1)^(n-j)*Binomial[If[j==0, 1, k^j], n-j], {j, 0, n-1}]];
Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Sep 21 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jul 07 2022
STATUS
approved