OFFSET
0,9
LINKS
Alois P. Heinz, Antidiagonals n = 0..140, flattened
Daniel Birmajer, Juan B. Gil, David S. Kenepp, and Michael D. Weiner, Restricted generating trees for weak orderings, arXiv:2108.04302 [math.CO], 2021.
FORMULA
E.g.f. of column k: 1/(1-Sum_{i=1..k} x^i/i!).
A(n,k) = Sum_{j=0..k} A276922(n,j).
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, 1, 1, 1, ...
0, 2, 3, 3, 3, 3, 3, 3, ...
0, 6, 12, 13, 13, 13, 13, 13, ...
0, 24, 66, 74, 75, 75, 75, 75, ...
0, 120, 450, 530, 540, 541, 541, 541, ...
0, 720, 3690, 4550, 4670, 4682, 4683, 4683, ...
0, 5040, 35280, 45570, 47110, 47278, 47292, 47293, ...
MAPLE
A:= proc(n, k) option remember; `if`(n=0, 1, add(
A(n-i, k)*binomial(n, i), i=1..min(n, k)))
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[n-i, k]*Binomial[n, i], {i, 1, Min[n, k]}]]; Table[A[n, d-n], {d, 0, 12}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 03 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 22 2016
STATUS
approved