A320983 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of nine.

0, 1, 10, 4116, 45431, 4619654, 56724741, 3604309466, 49361628592, 2539183745028, 38672184949164, 1795814647499288, 30258670886635123, 1339822976545126729, 24829628782352186543, 1080751193228180109916, 21899879370157544611142, 954090805109110152360526

Offset: 9

Author

Alois P. Heinz, Oct 25 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..451

Crossrefs

Column k=9 of A262125.

Cf. A262133, A262134.

Programs

Maple

b:= proc(u, o, c) option remember; `if`(c<0 or c>9, 0, `if`(u+o=0,
       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..9))(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, 9):
seq(a(n), n=9..30);

Formula

a(n) = A262134(n) - A262133(n).