A320984 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of ten.

0, 1, 11, 8220, 98827, 14052474, 185726938, 15068990276, 219771532102, 13747965316306, 220995092995233, 12094333663749818, 213504732754725133, 10896908531544406283, 210288454755592374452, 10376111829436767498058, 217839166931637914375624

Offset: 10

Author

Alois P. Heinz, Oct 25 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..451

Crossrefs

Column k=10 of A262125.

Cf. A262134, A262135.

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-> coeff(add(b(j-1, n-j, 0), j=1..n), x, 10):
seq(a(n), n=10..30);

Formula

a(n) = A262135(n) - A262134(n).