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%I #9 Sep 02 2017 16:04:01
%S 1,4,27,180,1015,5028,23051,101272,434835,1843320,7753471,32440884,
%T 135195307,561615460,2326740315,9617256944,39671268187,163352387952,
%U 671559953015,2756930503420,11303415274179,46290177094172,189368906605747,773942488240920,3160265160762575,12893881856438128,52567364492251191,214163336821005012,871950728486358835,3547937446945462500
%N The order of the semigroup of orientation-preserving or reserving full transformations of 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 31, table 3.4 and 3.5.
%F a(n) = A005430(n)-n*A006004(n).
%p A289718 := proc(n)
%p n*binomial(2*n,n)-n^2*(n^2-2*n+5)/2+n ;
%p end proc:
%K nonn,easy
%O 1,2
%A _R. J. Mathar_, Sep 02 2017