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

7,2

Links

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

Formula

a(n) = A262169(n) - A262168(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, 7)-b(n, 0$2, 6):
seq(a(n), n=7..24);

Crossrefs

Column k=7 of A258829.

Cf. A262168, A262169.

Sequence in context: A003396 A124899 A056852 * A300391 A126196 A182433

Adjacent sequences: A316391 A316392 A316393 * A316395 A316396 A316397

Keyword

nonn

Author

Alois P. Heinz, Jul 01 2018

Status

approved