A316395 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of eight.

1, 8, 1040, 9468, 507355, 5313447, 214378961, 2571977379, 92953037066, 1265907917962, 44038999833044, 674142774632948, 23379215615715958, 398561935596289153, 14037530250073013445, 264291741199540446059, 9551899031473405653870, 197148463934806397523934

Offset: 8

Author

Alois P. Heinz, Jul 01 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..451

Crossrefs

Column k=8 of A258829.

Cf. A262169, A262170.

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, 8)-b(n, 0$2, 7):
seq(a(n), n=8..25);

Formula

a(n) = A262170(n) - A262169(n).