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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.

%I A289711 #11 Sep 02 2017 15:48:41
%S A289711 1,1,1,1,6,2,1,21,36,3,1,60,288,96,4,1,155,1600,1200,200,5,1,378,7200,
%T A289711 9600,3600,360,6,1,889,28224,58800,39200,8820,588,7,1,2040,100352,
%U A289711 301056,313600,125440,18816,896,8,1,4599,331776,1354752,2032128,1270080,338688
%N A289711 Triangle T(n,p) read by rows: the order of the semigroup of orientation-preserving partial transformations of n elements with height p.
%H A289711 A. Umar, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Umar/umar2.html">Combinatorial Results for Semigroups of Orientation-Preserving Partial Transformations</a>, J. Int. Seq. 14 (2011) # 11.7.5, Corollary 10, Table 2.2
%e A289711 1 ;
%e A289711 1 1 ;
%e A289711 1 6 2 ;
%e A289711 1 21 36 3 ;
%e A289711 1 60 288 96 4;
%e A289711 1 155 1600 1200 200 5;
%e A289711 1 378 7200 9600 3600 360 6;
%e A289711 1 889 28224 58800 39200 8820 588 7;
%e A289711 1 2040 100352 301056 313600 125440 18816 896 8 ;
%e A289711 1 4599 331776 1354752 2032128 1270080 338688 36288 1296 9;
%e A289711 1 10230 1036800 5529600 11289600 10160640 4233600 806400 64800 1800 10 ;
%p A289711 A289711 := proc(n,p)
%p A289711     if p = 0 then
%p A289711         1;
%p A289711     elif p = 1 then
%p A289711         n*(2^n-1) ;
%p A289711     else
%p A289711         p*2^(n-p)*binomial(n,p)^2 ;
%p A289711     end if ;
%p A289711 end proc:
%Y A289711 Cf. A066524 (column p=1), A289713 (row sums).
%K A289711 tabl,nonn,easy
%O A289711 0,5
%A A289711 _R. J. Mathar_, Sep 02 2017