A262172 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 10.

1, 1, 2, 5, 20, 87, 522, 3271, 26168, 214955, 2149550, 21881102, 262573224, 3191352956, 44678941384, 631531613445, 10104505815120, 162875348137045, 2931756266466810, 53078841003479472, 1061576820069589440, 21327553502651079406, 469206177058323746932

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=10 of A262163.

Programs

Maple

b:= proc(u, o, c) option remember; `if`(c<0 or c>10, 0, `if`(u+o=0,
       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..10))(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, 10)))(b(0, n, 0)):
seq(a(n), n=0..25);

Formula

a(n) = A262163(n,10).