A130478 Triangle T(n,k) = n! / A130477(n,k).

1, 2, 2, 6, 3, 2, 24, 8, 3, 2, 120, 30, 8, 3, 2, 720, 144, 30, 8, 3, 2, 5040, 840, 144, 30, 8, 3, 2, 40320, 5760, 840, 144, 30, 8, 3, 2, 362880, 45360, 5760, 840, 144, 30, 8, 3, 2, 3628800, 403200, 45360, 5760, 840, 144, 30, 8, 3, 2

Offset

1,2

Comments

Sums of reciprocals of rows is 1. - Henry Bottomley, Nov 05 2009

Links

Table of n, a(n) for n=1..55.

Formula

T(n,k) = n! / A130477(n,k); such that by rows as vector terms, (n-th row of A130477) dot (n-th row of A130478) = n-th row of A130493 = n! repeated n times.

Triangle by rows = n! followed by the first (n-1) reversed terms of A001048: (2, 3, 8, 30, 144, 840, ...).

Left border = (1, 2, 6, 24, 120, ...); while all other columns = A001048: (2, 3, 8, 30, ...).

n-th row of the triangle = n terms of: (n!; (n-1)!+(n-2)!; (n-2)!+(n-3)!; ...; 1! + 0!).

Example

First few rows of the triangle:
     1;
     2,   2;
     6,   3,   2;
    24,   8,   3,  2;
   120,  30,   8,  3, 2;
   720, 144,  30,  8, 3, 2;
  5040, 840, 144, 30, 8, 3, 2;
  ...
Row 4 = (24, 8, 3, 2), terms such that (24, 8, 3, 2) dot (1, 3, 8, 12) = (24, 24, 24, 24), where (1, 3, 8, 12) = row 4 of A130477 and (24, 24, 24, 24) = row 4 of A130493.
Row 5 = (120, 30, 8, 3, 2) = 5! + (4!+3!) + (3!+2!) + (2!+1!) + (1!+1).
Row 5 = 120 followed by the first reversed 4 terms of A001048; i.e., 120 followed by 30, 8, 3, 2.

Crossrefs

Cf. A130493 (row sums), A001048, A130493, A130477.

Sequence in context: A377346 A355076 A344007 * A308140 A306464 A338449

Adjacent sequences: A130475 A130476 A130477 * A130479 A130480 A130481

Keyword

nonn,tabl

Author

Gary W. Adamson, May 31 2007

Extensions

Corrected and extended by Henry Bottomley, Nov 05 2009

Status

approved