A316397 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of ten.

1, 10, 4127, 45562, 4719041, 58003461, 3795919780, 52052335254, 2772611610514, 42268105493955, 2037044419366071, 34333238955892416, 1578674337291922196, 29239755067140936242, 1321207703588407017510, 26733500408009431631728, 1208079945873987947779946

Offset: 10

Author

Alois P. Heinz, Jul 01 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..451

Crossrefs

Column k=10 of A258829.

Cf. A262171, A262172.

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, 10)-b(n, 0$2, 9):
seq(a(n), n=10..26);

Formula

a(n) = A262172(n) - A262171(n).