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

10,3

Links

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

Formula

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

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);

Crossrefs

Column k=10 of A262125.

Cf. A262134, A262135.

Sequence in context: A199646 A214183 A214234 * A080050 A067254 A099806

Adjacent sequences: A320981 A320982 A320983 * A320985 A320986 A320987

Keyword

nonn

Author

Alois P. Heinz, Oct 25 2018

Status

approved