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

6,3

Links

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

Formula

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

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);

Crossrefs

Column k=6 of A262125.

Cf. A262130, A262131.

Sequence in context: A219873 A224469 A347907 * A080975 A003396 A124899

Adjacent sequences: A320977 A320978 A320979 * A320981 A320982 A320983

Keyword

nonn

Author

Alois P. Heinz, Oct 25 2018

Status

approved