A316394 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of seven.

1, 7, 522, 4260, 163871, 1572713, 49601660, 554432537, 16431601190, 211104220038, 6214132488281, 90601727479330, 2718687446733807, 44477388811619142, 1378374571651666083, 25055072909382001747, 807272266530396465622, 16165637154045080226474

Offset: 7

Author

Alois P. Heinz, Jul 01 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..451

Crossrefs

Column k=7 of A258829.

Cf. A262168, A262169.

Programs

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, 7)-b(n, 0$2, 6):
seq(a(n), n=7..24);

Formula

a(n) = A262169(n) - A262168(n).