A289718 The order of the semigroup of orientation-preserving or reserving full transformations of n elements.

1, 4, 27, 180, 1015, 5028, 23051, 101272, 434835, 1843320, 7753471, 32440884, 135195307, 561615460, 2326740315, 9617256944, 39671268187, 163352387952, 671559953015, 2756930503420, 11303415274179, 46290177094172, 189368906605747, 773942488240920, 3160265160762575, 12893881856438128, 52567364492251191, 214163336821005012, 871950728486358835, 3547937446945462500

Offset: 1

Author

R. J. Mathar, Sep 02 2017

Keywords

• nonn
• easy

Links

• A. Umar, Combinatorial Results for Semigroups of Orientation-Preserving Partial Transformations, J. Int. Seq. 14 (2011) # 11.7.5, corollary 31, table 3.4 and 3.5.

Programs

Maple

A289718 := proc(n)
     n*binomial(2*n,n)-n^2*(n^2-2*n+5)/2+n ;
end proc:

Formula

a(n) = A005430(n)-n*A006004(n).