0,3

Laradji, A. and Umar, A. Combinatorial results for the symmetric inverse semigroup. Semigroup Forum 75, (2007), 221-236.

a(n)=n!*sum(m=0,n-1,(-1^m/m!)sum(j=0,n-m,C(n-m)/j!)); (n-1)a(n)=n(2n-3)a(n-1)-n(n-1)(n-4)a(n-2)-n(n-1)(n-2)a(n-3), a(1)=1 and a(n)= 0 if n<1

a(3) = 12 because there are exactly 12 partial bijections (on a 3-element set) with exactly 1 fixed point, namely: (1)->(1), (2)->(2), (3)->(3), (1,2)->(1,3), (1,2)->(3,2), (1,3)->(1,2), (1,3)->(2,3), (2,3)->(2,1), (2,3)->(1,3), (1,2,3)->(1,3,2), (1,2,3)->(3,2,1), (1,2,3)->(2,1,3) - the mappings are coordinate-wise.

a(n) = A144088(n, 1) and a(n) = n*A144085(n-1)

Sequence in context: A062119 A052556 A052833 this_sequence A005443 A002867 A130426

Adjacent sequences: A144083 A144084 A144085 this_sequence A144087 A144088 A144089

nonn

A. Umar (aumarh(AT)squ.edu.om), Sep 10 2008, Sep 15 2008