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

9,3

Links

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

Formula

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

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);

Crossrefs

Column k=9 of A262125.

Cf. A262133, A262134.

Sequence in context: A291676 A249851 A024139 * A316397 A291332 A294747

Adjacent sequences: A320980 A320981 A320982 * A320984 A320985 A320986

Keyword

nonn

Author

Alois P. Heinz, Oct 25 2018

Status

approved