OFFSET
0,9
LINKS
Alois P. Heinz, Antidiagonals n = 0..140, flattened
Wikipedia, Permutation
FORMULA
E.g.f. of column k: (1-exp(-x))/(1-x)^(k+1).
A(n,k) = -1/k! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+k-j)!.
A(n,k) = A306234(n+k,k).
EXAMPLE
Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 3, 5, 7, 9, 11, 13, ...
4, 13, 28, 49, 76, 109, 148, ...
15, 67, 179, 375, 679, 1115, 1707, ...
76, 411, 1306, 3181, 6576, 12151, 20686, ...
455, 2921, 10757, 29843, 69299, 142205, 266321, ...
MAPLE
A:= (n, k)-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!:
seq(seq(A(n, d-n), n=0..d), d=0..12);
MATHEMATICA
m = 10;
col[k_] := col[k] = CoefficientList[(1-Exp[-x])/(1-x)^(k+1)+O[x]^(m+1), x]* Range[0, m]!;
A[n_, k_] := col[k][[n+1]];
Table[A[n, d-n], {d, 0, m}, {n, 0, d}] // Flatten (* Jean-François Alcover, May 03 2021 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Feb 23 2019
STATUS
approved