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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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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: A242108 A238941 A247582 * A271497 A293287 A236843

Adjacent sequences:  A224649 A224650 A224651 * A224653 A224654 A224655

KEYWORD

nonn,tabl

AUTHOR

Joerg Arndt, Apr 13 2013

STATUS

approved

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Last modified September 18 23:16 EDT 2021. Contains 347548 sequences. (Running on oeis4.)