A316396 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of nine.

1, 9, 2071, 20845, 1553153, 17662969, 908651571, 11670560732, 512693233164, 7392808621010, 303061463720474, 4869546964922509, 194661534866479194, 3459210686800253224, 138131753631241199208, 2695708505172764233290, 109038227244360661170616

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..451

Formula

a(n) = A262171(n) - A262170(n).

Maple

b:= proc(u, o, c, k) option remember;
      `if`(c<0 or c>k, 0, `if`(u+o=0, 1,
       add(b(u-j, o-1+j, c+1, k), j=1..u)+
       add(b(u+j-1, o-j, c-1, k), j=1..o)))
    end:
a:= n-> b(n, 0$2, 9)-b(n, 0$2, 8):
seq(a(n), n=9..25);

Crossrefs

Column k=9 of A258829.

Cf. A262170, A262171.

Sequence in context: A173281 A004820 A320982 * A162091 A172959 A250915

Adjacent sequences: A316393 A316394 A316395 * A316397 A316398 A316399

Keyword

nonn

Author

Alois P. Heinz, Jul 01 2018

Status

approved