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A316391 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of four. 2
1, 4, 62, 340, 4734, 33855, 495371, 4403025, 70083872, 746704117, 13023762276, 161905131484, 3091115525637, 43928623624790, 914530883776894, 14623431780216366, 330413968185491070, 5870376151413374683, 143271256595612492851, 2799645366893284489691 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..455

FORMULA

a(n) = A262166(n) - A262165(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, 4)-b(n, 0$2, 3):

seq(a(n), n=4..23);

CROSSREFS

Column k=4 of A258829.

Cf. A262165, A262166.

Sequence in context: A326225 A102193 A232156 * A293968 A222791 A166028

Adjacent sequences:  A316388 A316389 A316390 * A316392 A316393 A316394

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 01 2018

STATUS

approved

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Last modified January 24 20:52 EST 2022. Contains 350565 sequences. (Running on oeis4.)