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

0,4

Links

Table of n, a(n) for n=0..51.

Formula

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

Example

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;

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 *)

Crossrefs

Sequence in context: A059434 A292222 A182928 * A340114 A212360 A145888

Adjacent sequences: A141473 A141474 A141475 * A141477 A141478 A141479

Keyword

nonn,tabl

Author

Paul Curtz, Aug 09 2008

Extensions

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

Status

approved