OFFSET
0,9
LINKS
Alois P. Heinz, Antidiagonals n = 0..140, flattened
FORMULA
A(n,k) = Sum_{j=0..k} A292746(n,j).
A(n,k) = A(n,n) for all k >= n.
EXAMPLE
A(3,2) = 6: 3, 21a, 1a1a1a, 1a1a1b, 1a1b1a, 1a1b1b.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 3, 3, 3, 3, 3, 3, 3, ...
1, 3, 6, 7, 7, 7, 7, 7, 7, ...
2, 5, 13, 19, 20, 20, 20, 20, 20, ...
2, 7, 26, 52, 62, 63, 63, 63, 63, ...
4, 11, 54, 151, 217, 232, 233, 233, 233, ...
4, 15, 108, 442, 803, 944, 965, 966, 966, ...
7, 22, 219, 1314, 3092, 4158, 4425, 4453, 4454, ...
MAPLE
f:= (n, k)-> add(Stirling2(n, j), j=0..k):
b:= proc(n, i, k) option remember; `if`(n=0 or i<2,
f(n, k), add(b(n-i*j, i-1, k), j=0..n/i))
end:
A:= (n, k)-> b(n$2, k):
seq(seq(A(n, d-n), n=0..d), d=0..14);
MATHEMATICA
f[n_, k_] := Sum[StirlingS2[n, j], {j, 0, k}];
b[n_, i_, k_] := b[n, i, k] = If[n == 0 || i < 2, f[n, k], Sum[b[n - i*j, i - 1, k], {j, 0, n/i}]];
A[n_, k_] := b[n, n, k];
Table[A[n, d - n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, May 17 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 22 2017
STATUS
approved