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A316390 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of three. 2
1, 3, 28, 130, 1263, 8090, 88101, 724189, 8887448, 89401804, 1229179691, 14638611036, 223711095367, 3078744103979, 51892788554614, 810254535452378, 14955918856848519, 261173044555806630, 5245841953983851853, 101285541723126490941, 2201267668629421856324 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..458

FORMULA

a(n) = A262165(n) - A262164(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, 3)-b(n, 0$2, 2):

seq(a(n), n=3..23);

CROSSREFS

Column k=3 of A258829.

Cf. A262164, A262165.

Sequence in context: A338791 A100019 A053132 * A048367 A095665 A145346

Adjacent sequences:  A316387 A316388 A316389 * A316391 A316392 A316393

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 01 2018

STATUS

approved

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Last modified May 14 22:40 EDT 2021. Contains 343909 sequences. (Running on oeis4.)