A262168 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 6.

1, 1, 2, 5, 20, 87, 522, 3270, 26160, 214424, 2144240, 21705682, 260468184, 3134839134, 43887747876, 611561379844, 9784982077504, 154830562162384, 2786950118922912, 49340681212898288, 986813624257965760, 19321622221580752560, 425075688874776556320

Offset: 0

Author

Alois P. Heinz, Sep 13 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..452

Crossrefs

Column k=6 of A262163.

Programs

Maple

b:= proc(u, o, c) option remember; `if`(c<0 or c>6, 0, `if`(u+o=0,
       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..6))(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, 6)))(b(0, n, 0)):
seq(a(n), n=0..25);

Formula

a(n) = A262163(n,6).