1,2

Row sums = A130494: (1, 4, 11, 37, 163,...).

Triangle(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 A130478 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! + 1).

First few rows of the triangle are:

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.

Cf. A130493, A001048, A130493, A130477.

Sequence in context: A013608 A130674 A100346 this_sequence A128623 A085738 A100641

Adjacent sequences: A130475 A130476 A130477 this_sequence A130479 A130480 A130481

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), May 31 2007