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

1,5

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.

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.

Example

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;
...

Crossrefs

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

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

Sequence in context: A238941 A247582 A359795 * A271497 A293287 A236843

Adjacent sequences: A224649 A224650 A224651 * A224653 A224654 A224655

Keyword

nonn,tabl

Author

Joerg Arndt, Apr 13 2013

Status

approved