A122844 Triangle read by rows: T[n,k] = the number of ascending runs of length at least k in the permutations of [n] for k <= n.

1, 3, 1, 12, 5, 1, 60, 28, 7, 1, 360, 180, 50, 9, 1, 2520, 1320, 390, 78, 11, 1, 20160, 10920, 3360, 714, 112, 13, 1, 181440, 100800, 31920, 7056, 1176, 152, 15, 1, 1814400, 1028160, 332640, 75600, 13104, 1800, 198, 17, 1

Offset: 1

Author

David Scambler, Sep 13 2006

Keywords

• easy
• nonn
• tabl

Comments

Column T[n,1] is essentially A001710 - all ascending runs in permutations of [n] Column T[n,2] is A006157 - ascending runs of length at least 2 in permutations of [n] Column T[n,3] is A005460 - ascending runs of length at least 3 in permutations of [n]

Examples

			1
3 1
12 5 1 ; there are 5 ascending runs of length at least 2 in the permutations of [3], namely 13 in 132 and in 213, 23 in 231, 12 in 312, 123 in 123. T[3,2] = 5.
		

Crossrefs

Cf. A122844, A001710, A006157, A005460.

Formula

T[n,k] = n![k(n-k+1)+1]/(k+1)! for 0A122843(n,j) (partial row sums of A122843)