A316393 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of six.

1, 6, 261, 1890, 52022, 455231, 11174035, 116105272, 2810232512, 34036483163, 844691910962, 11731978216291, 303637667232802, 4769379288424677, 129700918311614279, 2277005590881369266, 65261900211279910831, 1267764017301809851710, 38324737795523150842616

Offset: 6

Author

Alois P. Heinz, Jul 01 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..452

Crossrefs

Column k=6 of A258829.

Cf. A262167, A262168.

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, 6)-b(n, 0$2, 5):
seq(a(n), n=6..24);

Formula

a(n) = A262168(n) - A262167(n).