A289710 Triangle T(n,r) read by rows: order of the semigroup of orientation-preserving partial transformations of n elements with breath r.

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

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: A080721 A123588 A373504 * A243594 A360707 A365674

Adjacent sequences: A289707 A289708 A289709 * A289711 A289712 A289713

Keyword

tabl,nonn,easy

Author

R. J. Mathar, Sep 02 2017

Status

approved