A100711 Table read by antidiagonals: T(m,n) gives the ordinal number in the table of permutations of length n+1 of the permutation which reverses the first m+1 items on a list of length n+1, leaving the remaining items unaltered. For example, T(5,7) is 28494 and the 28494th row of the permutation table of order 8 is 5 4 3 2 1 0 6 7.

1, 2, 0, 6, 5, 0, 24, 14, 0, 0, 120, 54, 23, 0, 0, 720, 264, 86, 0, 0, 0, 5040, 1560, 414, 119, 0, 0, 0, 40320, 10800, 2424, 566, 0, 0, 0, 0, 85680, 16680, 3294, 719, 0, 0, 0, 131760, 22584, 4166, 0, 0, 0, 177960, 28494, 5039, 0, 0, 224184, 34406, 0, 0, 270414, 40319, 0

Offset: 1

Author

Eugene McDonnell (eemcd(AT)mac.com), Dec 10 2004

Keywords

• easy
• nonn
• tabl

Comments

The first 8 rows and columns of T are:

1 2 6 24 120 720 5040 40320

0 5 14 54 264 1560 10800 85680

0 0 23 86 414 2424 16680 131760

0 0 0 119 566 3294 22584 177960

0 0 0 0 719 4166 28494 224184

0 0 0 0 0 5039 34406 270414

0 0 0 0 0 0 40319 316646

0 0 0 0 0 0 0 362879

Examples

			T(5,7) is 28494 because we can write (5,4,3,2,1) dot (7!,6!,5!,4!.3!), or (5,4,3,2,1) dot (5040,720,120,24,6) or 28494.
		

Crossrefs

See A100630 for another version.

Formula

T(m, n) is given by the dot product of (m, m-1, m-2, ..., 1) and (n!, (n-1)!, ..., (1+n-m)!).