OFFSET
0,8
LINKS
Alois P. Heinz, Antidiagonals n = 0..140, flattened
FORMULA
G.f. of column k: 1/(1 + Sum_{j=1..k} (k+1-j)*(-x)^j).
EXAMPLE
A(3,3) = 16: 000, 002, 020, 021, 022, 100, 102, 110, 111, 200, 202, 210, 211, 220, 221, 222 (using ternary alphabet {0, 1, 2}).
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, 7, ...
0, 1, 3, 7, 13, 21, 31, 43, ...
0, 1, 4, 16, 42, 88, 160, 264, ...
0, 1, 5, 37, 136, 369, 826, 1621, ...
0, 1, 6, 86, 440, 1547, 4264, 9953, ...
0, 1, 7, 200, 1423, 6486, 22012, 61112, ...
0, 1, 8, 465, 4602, 27194, 113632, 375231, ...
MAPLE
A:= proc(n, k) option remember; `if`(n<0, 0, `if`(n=0, 1,
-add((-1)^j*(k+1-j)*A(n-j, k), j=1..k)))
end:
seq(seq(A(n, d-n), n=0..d), d=0..14);
MATHEMATICA
A[n_, k_] := A[n, k] = If[n < 0, 0, If[n == 0, 1, -Sum[(-1)^j*(k + 1 - j)* A[n-j, k], {j, 1, k}]]];
Table[A[n, d-n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, Jun 08 2018, from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Oct 26 2016
STATUS
approved