A316397 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of ten.

1, 10, 4127, 45562, 4719041, 58003461, 3795919780, 52052335254, 2772611610514, 42268105493955, 2037044419366071, 34333238955892416, 1578674337291922196, 29239755067140936242, 1321207703588407017510, 26733500408009431631728, 1208079945873987947779946

Offset

10,2

Links

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

Formula

a(n) = A262172(n) - A262171(n).

Maple

b:= proc(u, o, c, k) option remember;
      `if`(c<0 or c>k, 0, `if`(u+o=0, 1,
       add(b(u-j, o-1+j, c+1, k), j=1..u)+
       add(b(u+j-1, o-j, c-1, k), j=1..o)))
    end:
a:= n-> b(n, 0$2, 10)-b(n, 0$2, 9):
seq(a(n), n=10..26);

Crossrefs

Column k=10 of A258829.

Cf. A262171, A262172.

Sequence in context: A249851 A024139 A320983 * A291332 A294747 A199354

Adjacent sequences: A316394 A316395 A316396 * A316398 A316399 A316400

Keyword

nonn

Author

Alois P. Heinz, Jul 01 2018

Status

approved