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A289710 Triangle T(n,r) read by rows: order of the semigroup of orientation-preserving partial transformations of n elements with breath r. 2
1, 1, 1, 1, 4, 4, 1, 9, 27, 24, 1, 16, 96, 208, 128, 1, 25, 250, 950, 1325, 610, 1, 36, 540, 3120, 7290, 7416, 2742, 1, 49, 1029, 8330, 28665, 47922, 38563, 11970, 1, 64, 1792, 19264, 90720, 219968, 287168, 191808, 51424, 1, 81, 2916, 40068, 246078, 806274, 1509732, 1619676, 926073, 218718 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..54.

A. Umar, Combinatorial Results for Semigroups of Orientation-Preserving Partial Transformations, J. Int. Seq. 14 (2011) # 11.7.5, Corollary 9, Table 2.1

EXAMPLE

1 ;

1 1;

1 4 4;

1 9 27 24;

1 16 96 208 128;

1 25 250 950 1325 610;

1 36 540 3120 7290 7416 2742;

1 49 1029 8330 28665 47922 38563 11970;

1 64 1792 19264 90720 219968 287168 191808 51424;

1 81 2916 40068 246078 806274 1509732 1619676 926073 218718;

MAPLE

A289710 := proc(n, r)

    if r = 0 then

        1;

    else

        r*binomial(n, r)*binomial(n+r-1, n-1)-n*(r-1)*binomial(n, r) ;

    end if ;

end proc:

CROSSREFS

Cf. A092364 (column r=2), A289713 (row sums)

Sequence in context: A179399 A080721 A123588 * A243594 A106026 A096078

Adjacent sequences:  A289707 A289708 A289709 * A289711 A289712 A289713

KEYWORD

tabl,nonn,easy

AUTHOR

R. J. Mathar, Sep 02 2017

STATUS

approved

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Last modified November 13 02:59 EST 2019. Contains 329085 sequences. (Running on oeis4.)