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

Author

Alois P. Heinz, Jul 01 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=9 of A258829.

Cf. A262170, A262171.

Programs

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);

Formula

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