

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
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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, (nth row of A130477) dot (nth row of A130478) = nth row of A130493 = n! repeated n times. Triangle A130478 by rows = n! followed by the first (n1)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,...). nth row of the triangle = n terms of: (n!; (n1!)+(n2!); (n2!)+(n3!);...+ (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



