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A320977 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of three. 2
0, 1, 4, 57, 311, 3857, 27589, 355751, 3185258, 44435241, 479927081, 7311147055, 92603527295, 1540826943617, 22398016781688, 405865410503155, 6658173453910401, 130871330990044897, 2390845313044048301, 50759828657781860167, 1021623022236754343662 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

LINKS

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

FORMULA

a(n) = A262128(n) - A262126(n).

MAPLE

b:= proc(u, o, c) option remember; `if`(c<0 or c>3, 0, `if`(u+o=0,

       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..3))(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, 3):

seq(a(n), n=3..30);

CROSSREFS

Column k=3 of A262125.

Cf. A262126, A262128.

Sequence in context: A181437 A353001 A156873 * A071540 A298764 A299562

Adjacent sequences:  A320974 A320975 A320976 * A320978 A320979 A320980

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 25 2018

STATUS

approved

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Last modified May 28 09:09 EDT 2022. Contains 354112 sequences. (Running on oeis4.)