A122823 Triangle read by rows: T(n,k) = count of increasing runs in two concatenated k-permutations of [n].

2, 7, 11, 15, 96, 132, 26, 378, 2088, 2664, 40, 1040, 12960, 66240, 80640, 57, 2325, 51600, 594000, 2894400, 3412800, 77, 4536, 157500, 3225600, 35380800, 166924800, 192326400, 100, 8036, 402192, 12877200, 251193600, 2667168000, 12294374400

Offset: 1

Author

David Scambler, Oct 29 2006

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins:
2
7 11
15 96 132
Take the 2-permutations of [2] namely 12 and 21 and form all possible strings that are concatenations of two 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

Column 1 = T(n, 1) = A005449, Second pentagonal numbers: n*(3n+1)/2.

Formula

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