A320980 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of six.

0, 1, 7, 514, 4189, 154261, 1477381, 44169020, 493190771, 13821362271, 177705152975, 4949371839867, 72355179873697, 2058206624313873, 33818827542140211, 995975339452380880, 18206096557050382759, 558929622195992201388, 11264684856271486133087

Offset: 6

Author

Alois P. Heinz, Oct 25 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..452

Crossrefs

Column k=6 of A262125.

Cf. A262130, A262131.

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-> coeff(add(b(j-1, n-j, 0), j=1..n), x, 6):
seq(a(n), n=6..30);

Formula

a(n) = A262131(n) - A262130(n).