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A262164 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 2. 3
1, 1, 2, 4, 16, 54, 324, 1532, 12256, 74512, 745120, 5536752, 66441024, 583466480, 8168530720, 82769713504, 1324315416064, 15208157533440, 273746835601920, 3513491887566848, 70269837751336960, 996837786288583168, 21930431298348829696, 340730692136161864704 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..464

FORMULA

a(n) = A262163(n,2).

MAPLE

b:= proc(u, o, c) option remember; `if`(c<0 or c>2, 0, `if`(u+o=0,

       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..2))(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-> (p-> add(coeff(p, x, i), i=0..min(n, 2)))(b(0, n, 0)):

seq(a(n), n=0..25);

CROSSREFS

Column k=2 of A262163.

Sequence in context: A284730 A255730 A010362 * A322940 A306519 A001472

Adjacent sequences:  A262161 A262162 A262163 * A262165 A262166 A262167

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 13 2015

STATUS

approved

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Last modified June 19 06:47 EDT 2019. Contains 324218 sequences. (Running on oeis4.)