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%I #9 Sep 02 2017 15:54:08
%S 1,4,24,128,610,2742,11970,51424,218718,923690,3879766,16224804,
%T 67603744,280816018,1163381190,4808642880,19835652598,81676217394,
%U 335780005758,1378465287820,5651707681200,23145088600458,94684453366894,386971244196648,1580132580471300,6446940928324702
%N The order of the semigroup of orientation-preserving full transformations on n elements.
%H 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 17, table 2.4, table 2.5.
%F a(n) = A002457(n-1)-A002378(n-1).
%F (n-1)*(3*n-10)*a(n) +6*(-3*n^2+12*n-8)*a(n-1) +3*(9*n^2-35*n+32)*a(n-2) -2*(3*n-4)*(2*n-5)*a(n-3)=0.
%p A289715 := proc(n)
%p n/2*binomial(2*n,n)-n*(n-1) ;
%p end proc:
%K nonn,easy
%O 1,2
%A _R. J. Mathar_, Sep 02 2017
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