A289715 The order of the semigroup of orientation-preserving full transformations on n elements.

1, 4, 24, 128, 610, 2742, 11970, 51424, 218718, 923690, 3879766, 16224804, 67603744, 280816018, 1163381190, 4808642880, 19835652598, 81676217394, 335780005758, 1378465287820, 5651707681200, 23145088600458, 94684453366894, 386971244196648, 1580132580471300, 6446940928324702

Offset

1,2

Links

Table of n, a(n) for n=1..26.

A. Umar, Combinatorial Results for Semigroups of Orientation-Preserving Partial Transformations, J. Int. Seq. 14 (2011) # 11.7.5, corollary 17, table 2.4, table 2.5.

Formula

a(n) = A002457(n-1)-A002378(n-1).

(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.

Maple

A289715 := proc(n)
    n/2*binomial(2*n, n)-n*(n-1) ;
end proc:

Crossrefs

Sequence in context: A339123 A024049 A103455 * A174443 A180222 A192070

Adjacent sequences: A289712 A289713 A289714 * A289716 A289717 A289718

Keyword

nonn,easy

Author

R. J. Mathar, Sep 02 2017

Status

approved