A316392 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of five.

1, 5, 129, 819, 16066, 127538, 2423226, 23367449, 459383574, 5246611332, 109138956326, 1446115120862, 32069014233249, 484780196858918, 11478459399841878, 195255855453716821, 4931560739013573590, 93326559046408832001, 2509294817575539112099

Offset: 5

Author

Alois P. Heinz, Jul 01 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..453

Crossrefs

Column k=5 of A258829.

Cf. A262166, A262167.

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, 5)-b(n, 0$2, 4):
seq(a(n), n=5..23);

Formula

a(n) = A262167(n) - A262166(n).