OFFSET
0,9
COMMENTS
Column k > 0 is asymptotic to exp(k-1) * n!. - Vaclav Kotesovec, Sep 22 2016
LINKS
Alois P. Heinz, Antidiagonals n = 0..42, flattened
FORMULA
A(n,k) = Sum_{j=0..k} A276891(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, 10, 13, 13, 13, 13, 13, ...
0, 24, 44, 62, 75, 75, 75, 75, ...
0, 120, 234, 352, 466, 541, 541, 541, ...
0, 720, 1470, 2348, 3272, 4142, 4683, 4683, ...
0, 5040, 10656, 17880, 26032, 34792, 42610, 47293, ...
MAPLE
b:= proc(n, m, l) option remember; `if`(n=0, m!,
add(b(n-1, max(m, j), [subsop(1=NULL, l)[],
`if`(j<=m, 0, j)]), j={l[], m+1} minus {0}))
end:
A:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0),
`if`(k=1, n!, b(n, 0, [0$(k-1)]))):
seq(seq(A(n, d-n), n=0..d), d=0..12);
MATHEMATICA
b[n_, m_, l_List] := b[n, m, l] = If[n == 0, m!, Sum[b[n - 1, Max[m, j], Append[ReplacePart[l, 1 -> Nothing], If[j <= m, 0, j]]], {j, Append[l, m + 1] ~Complement~ {0}}]]; A[n_, k_] := If[k==0, If[n==0, 1, 0], If[k==1, n!, b[n, 0, Array[0&, k-1]]]]; Table[A[n, d-n], {d, 0, 12}, {n, 0, d}] // Flatten (* Jean-François Alcover, Jan 06 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 21 2016
STATUS
approved