A141476 Triangle T(n,k) = A000142(n-k)*A003319(k+1) read by rows.

1, 1, 1, 2, 1, 3, 6, 2, 3, 13, 24, 6, 6, 13, 71, 120, 24, 18, 26, 71, 461, 720, 120, 72, 78, 142, 461, 3447, 5040, 720, 360, 312, 426, 922, 3447, 29093, 40320, 5040, 2160, 1560, 1704, 2766, 6894, 29093, 273343, 362880, 40320, 15120, 9360, 8520, 11064, 20682

Offset: 0

Author

Paul Curtz, Aug 09 2008

Keywords

• nonn
• tabl

Examples

			The triangle starts at row n=0 with columns 0 <= k <= n:
    1;
    1,   1;
    2,   1,   3;
    6,   2,   3,  13;
   24,   6,   6,  13,  71;
  120,  24,  18,  26,  71, 461;
		

Programs

Mathematica

(* b = A003319 *) b[0]=0; b[n_] := b[n] = n! - Sum[k!*b[n-k], {k, 1, n-1}];
T[n_, k_] := (n-k)! b[k+1]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 18 2018 *)

Formula

Row sums: Sum_{k=0..n} T(n,k) = A000142(n+1) = (n+1)!.

Extensions

Edited and extended by R. J. Mathar, Dec 05 2008