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A130478 Triangle T(n,k) = n! / A130477(n,k). 7
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

LINKS

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

FORMULA

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).

EXAMPLE

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.

CROSSREFS

Cf. A130493, A001048, A130493, A130477.

Sequence in context: A319708 A230266 A329380 * A308140 A306464 A163890

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

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Last modified January 23 04:16 EST 2020. Contains 331168 sequences. (Running on oeis4.)