OFFSET
0,6
LINKS
Alois P. Heinz, Antidiagonals n = 0..140, flattened
FORMULA
A(n,k) = n! * [x^n] (exp(x)-x^k/k!)^n.
EXAMPLE
Square array A(n,k) begins:
0 : 1, 1, 1, 1, 1, 1, 1, ...
1 : 1, 0, 1, 1, 1, 1, 1, ...
2 : 2, 2, 2, 4, 4, 4, 4, ...
3 : 6, 3, 9, 24, 27, 27, 27, ...
4 : 24, 40, 76, 208, 252, 256, 256, ...
5 : 120, 205, 825, 2325, 3025, 3120, 3125, ...
6 : 720, 2556, 10206, 31956, 44406, 46476, 46650, ...
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0 and i=0, 1,
`if`(i<1, 0, add(`if`(j=k, 0, b(n-j, i-1, k)*
binomial(n, j)), j=0..n)))
end:
A:= (n, k)-> b(n$2, k):
seq(seq(A(n, d-n), n=0..d), d=0..14);
MATHEMATICA
nn = n; f[m_]:=Flatten[Table[m[[j, i - j + 1]], {i, 1, Length[m]}, {j, 1, i}]]; f[Transpose[Table[Prepend[Table[n! Coefficient[Series[(Exp[x] -x^k/k!)^n, {x, 0, nn}], x^n], {n, 1, 10}], 1], {k, 0, 10}]]] (* Geoffrey Critzer, Jan 31 2015 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jul 21 2014
STATUS
approved