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A289711 Triangle T(n,p) read by rows: the order of the semigroup of orientation-preserving partial transformations of n elements with height p. 2
1, 1, 1, 1, 6, 2, 1, 21, 36, 3, 1, 60, 288, 96, 4, 1, 155, 1600, 1200, 200, 5, 1, 378, 7200, 9600, 3600, 360, 6, 1, 889, 28224, 58800, 39200, 8820, 588, 7, 1, 2040, 100352, 301056, 313600, 125440, 18816, 896, 8, 1, 4599, 331776, 1354752, 2032128, 1270080, 338688 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..51.

A. Umar, Combinatorial Results for Semigroups of Orientation-Preserving Partial Transformations, J. Int. Seq. 14 (2011) # 11.7.5, Corollary 10, Table 2.2

EXAMPLE

1 ;

1 1 ;

1 6 2 ;

1 21 36 3 ;

1 60 288 96 4;

1 155 1600 1200 200 5;

1 378 7200 9600 3600 360 6;

1 889 28224 58800 39200 8820 588 7;

1 2040 100352 301056 313600 125440 18816 896 8 ;

1 4599 331776 1354752 2032128 1270080 338688 36288 1296 9;

1 10230 1036800 5529600 11289600 10160640 4233600 806400 64800 1800 10 ;

MAPLE

A289711 := proc(n, p)

    if p = 0 then

        1;

    elif p = 1 then

        n*(2^n-1) ;

    else

        p*2^(n-p)*binomial(n, p)^2 ;

    end if ;

end proc:

CROSSREFS

Cf. A066524 (column p=1), A289713 (row sums).

Sequence in context: A002247 A124913 A181415 * A101818 A138186 A110321

Adjacent sequences:  A289708 A289709 A289710 * A289712 A289713 A289714

KEYWORD

tabl,nonn,easy

AUTHOR

R. J. Mathar, Sep 02 2017

STATUS

approved

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Last modified August 4 18:15 EDT 2021. Contains 346455 sequences. (Running on oeis4.)