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A320980 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of six. 2
0, 1, 7, 514, 4189, 154261, 1477381, 44169020, 493190771, 13821362271, 177705152975, 4949371839867, 72355179873697, 2058206624313873, 33818827542140211, 995975339452380880, 18206096557050382759, 558929622195992201388, 11264684856271486133087 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..452

FORMULA

a(n) = A262131(n) - A262130(n).

MAPLE

b:= proc(u, o, c) option remember; `if`(c<0 or c>6, 0, `if`(u+o=0,

       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..6))(add(

       b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))

    end:

a:= n-> coeff(add(b(j-1, n-j, 0), j=1..n), x, 6):

seq(a(n), n=6..30);

CROSSREFS

Column k=6 of A262125.

Cf. A262130, A262131.

Sequence in context: A219873 A224469 A347907 * A080975 A003396 A124899

Adjacent sequences:  A320977 A320978 A320979 * A320981 A320982 A320983

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 25 2018

STATUS

approved

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)