A262170 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 8.

1, 1, 2, 5, 20, 87, 522, 3271, 26168, 214954, 2149540, 21879021, 262548252, 3189754241, 44656559374, 630564958413, 10089039334608, 162310602568627, 2921590846235286, 52733511434265043, 1054670228685300860, 21098558728828707796, 464168292034231571512

Offset: 0

Author

Alois P. Heinz, Sep 13 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Column k=8 of A262163.

Programs

Maple

b:= proc(u, o, c) option remember; `if`(c<0 or c>8, 0, `if`(u+o=0,
       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..8))(add(
       b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
    end:
a:= n-> (p-> add(coeff(p, x, i), i=0..min(n, 8)))(b(0, n, 0)):
seq(a(n), n=0..25);

Formula

a(n) = A262163(n,8).