A289711 Triangle T(n,p) read by rows: the order of the semigroup of orientation-preserving partial transformations of n elements with height p.

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

Offset: 0

Author

R. J. Mathar, Sep 02 2017

Keywords

• tabl
• nonn
• easy

Examples

			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 ;
		

Links

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

Crossrefs

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

Programs

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: