A262171 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 9.

1, 1, 2, 5, 20, 87, 522, 3271, 26168, 214955, 2149549, 21881092, 262569097, 3191307394, 44674222343, 631473609984, 10100709895340, 162823295801791, 2928983654856296, 53036572897985517, 1059539775650223369, 21293220263695186990, 467627502721031824736

Offset: 0

Author

Alois P. Heinz, Sep 13 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Column k=9 of A262163.

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-> (p-> add(coeff(p, x, i), i=0..min(n, 9)))(b(0, n, 0)):
seq(a(n), n=0..25);

Formula

a(n) = A262163(n,9).