A112858 Table read by antidiagonals: T(n,k) = count of increasing runs in strings of length n*k formed by concatenating k permutations of [n].

1, 2, 3, 3, 11, 12, 4, 32, 132, 60, 5, 84, 1152, 2664, 360, 6, 208, 9072, 93312, 80640, 2520, 7, 496, 67392, 2944512, 14169600, 3412800, 20160, 8, 1152, 482112, 87588864, 2239488000, 3608064000, 192326400, 181440, 9, 2624, 3359232, 2508226560

Offset: 1

Author

David Scambler, Nov 22 2006

Keywords

• easy
• nonn
• tabl

Comments

The first column T(n,1) is A001710(n+1), i.e., (n+1)!/2. The 2nd column T(n,2) is the outer diagonal of triangle A122823.

Examples

			Table begins:
   1    2     3       4 ...
   3   11    32      84 ...
  12  132  1152    9072 ...
  60 2664 93312 2944512 ...
  ...
Example: Take the permutations of [2], namely, 12 and 21, and form all possible strings that are concatenations of 2 of these permutations. These are 1212, 1221, 2112, 2121 with 2, 3, 3, 3 increasing runs respectively. T(2,2) = 2 + 3 + 3 + 3 = 11.
		

Crossrefs

Cf. A001710, A110952, A122823.

Formula

T(n,k) = (k(n+1)/2 - (k-1)(n-1)/2n) * (n!)^k.