A224652 Triangle read by rows: T(n,k) is the number of permutations of n elements with k the (smallest) header (first element) of the longest descending subsequence.

1, 1, 1, 1, 2, 3, 1, 5, 8, 10, 1, 14, 25, 35, 45, 1, 42, 89, 141, 196, 251, 1, 132, 357, 644, 966, 1302, 1638, 1, 429, 1602, 3284, 5300, 7526, 9878, 12300, 1, 1430, 7959, 18423, 31947, 47859, 65619, 84765, 104877, 1, 4862, 43127, 112255, 209500, 331795, 475738, 637657, 813730, 1000135

Offset: 1

Author

Joerg Arndt, Apr 13 2013

Keywords

• nonn
• tabl

Comments

Table II "Distribution of F_n" on p. 99 of the Pilpel reference.

Column 2 is A000108; column 3 is A006219; the diagonal is A006220; the row sums are A000142.

Examples

			Triangle begins
1;
1, 1;
1, 2, 3;
1, 5, 8, 10;
1, 14, 25, 35, 45;
1, 42, 89, 141, 196, 251;
1, 132, 357, 644, 966, 1302, 1638;
1, 429, 1602, 3284, 5300, 7526, 9878, 12300;
1, 1430, 7959, 18423, 31947, 47859, 65619, 84765, 104877;
1, 4862, 43127, 112255, 209500, 331795, 475738, 637657, 813730, 1000135;
...
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..91
• S. Pilpel, Descending subsequences of random permutations, J. Combin. Theory, A 53 (1990), 96-116.

Crossrefs

Cf. A000108, A006219, A006220, A000142 (row sums).

Cf. A047874 (Table I, "Distribution of L_n" on p. 99 of the Pilpel reference).