OFFSET
0,9
LINKS
Alois P. Heinz, Antidiagonals n = 0..99, flattened
EXAMPLE
Table begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
1, 3, 3, 3, 3, 3, ...
1, 16, 19, 22, 25, 28, ...
1, 125, 185, 253, 329, 413, ...
1, 1296, 2541, 4256, 6471, 9216, ...
MAPLE
A:= proc(n, k) option remember; if n<=0 or k=0 then 1 else A(n-1, k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp(x*%), x, n+1), polynom), x) end: T:= (n, k)-> coeff(A(n, k)(x), x, n)*n!: seq(seq(T(n, d-n), n=0..d), d=0..11);
MATHEMATICA
a[n_, k_][x_] := Module[{f}, f = If[n <= 0 || k == 0, 1, a[n-1, k][((#+1)^k-1)/k]]&; Normal[Series[Exp[y*f[y]], {y, 0, n+1}]] /. y -> x]; t[n_, k_] := Coefficient[a[n, k][x], x, n]*n!; Table[t[n, d-n], {d, 0, 11}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 12 2014, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Aug 27 2008
STATUS
approved