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

5,2

Links

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

Formula

a(n) = A262167(n) - A262166(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, 5)-b(n, 0$2, 4):
seq(a(n), n=5..23);

Crossrefs

Column k=5 of A258829.

Cf. A262166, A262167.

Sequence in context: A224250 A316986 A355085 * A277259 A230303 A094074

Adjacent sequences: A316389 A316390 A316391 * A316393 A316394 A316395

Keyword

nonn

Author

Alois P. Heinz, Jul 01 2018

Status

approved