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A289714 Triangle T(n,k) read by rows: the number of semigroups of orientation-preserving partial transformations on n element with right waist k. 1
1, 1, 1, 1, 3, 5, 1, 7, 19, 34, 1, 15, 63, 135, 235, 1, 31, 191, 471, 911, 1556, 1, 63, 543, 1503, 3183, 5883, 9969, 1, 127, 1471, 4495, 10319, 20483, 37031, 62602, 1, 255, 3839, 12799, 31615, 67007, 128607, 229743, 388343, 1, 511, 9727, 35071, 92671, 208735, 423583, 796687, 1412863, 2389768, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..55.

A. Umar, Combinatorial Results for Semigroups of Orientation-Preserving Partial Transformations, J. Int. Seq. 14 (2011) # 11.7.5

EXAMPLE

1 ;

1 1 ;

1 3 5 ;

1 7 19 34 ;

1 15 63 135 235;

1 31 191 471 911 1556 ;

1 63 543 1503 3183 5883 9969 ;

1 127 1471 4495 10319 20483 37031 62602 ;

1 255 3839 12799 31615 67007 128607 229743 388343 ;

1 511 9727 35071 92671 208735 423583 796687 1412863 2389768 ;

1 1023 24063 93183 262143 625023 1336383 2638143 4894623 8637363 14621533 ;

MAPLE

A289714 := proc(n, k)

    if k = 0 then

        1;

    else

        n*add(binomial(n-1, r-1)*binomial(r+k-2, r-1), r=1..n)-(n-2)*2^(n-1)-1 ;

    end if ;

end proc:

CROSSREFS

Cf. A289713 (row sums), A000225 (column 1), A053545 (column 2)

Sequence in context: A208509 A086233 A318190 * A242390 A065395 A236631

Adjacent sequences:  A289711 A289712 A289713 * A289715 A289716 A289717

KEYWORD

nonn,tabl,easy

AUTHOR

R. J. Mathar, Sep 02 2017

STATUS

approved

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Last modified September 21 00:17 EDT 2019. Contains 327252 sequences. (Running on oeis4.)