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

8,2

Links

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

Formula

a(n) = A262170(n) - A262169(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, 8)-b(n, 0$2, 7):
seq(a(n), n=8..25);

Crossrefs

Column k=8 of A258829.

Cf. A262169, A262170.

Sequence in context: A076688 A004808 A320981 * A176372 A047943 A089672

Adjacent sequences: A316392 A316393 A316394 * A316396 A316397 A316398

Keyword

nonn

Author

Alois P. Heinz, Jul 01 2018

Status

approved