[seqfan] A000698 == indecomposable fixed-point free involutions of {2n}?
Joerg Arndt
arndt at jjj.de
Wed Dec 29 15:36:54 CET 2010
It appears that
http://oeis.org/A000698
gives the numbers of fixed-point free involutions of {1,2,...,2*n}
( see http://oeis.org/A001147 )
that are indecomposable (connected), see
http://oeis.org/A003319
Accepting the above, the number of fixed-point free involutions
of {2n} that ARE decomposable are
[0, 0, 1, 5, 31, 239, 2233, 24725, 318631, 4707359, 78691633]
which is
http://oeis.org/draft/A177797
As PARI code:
f(n)=(2*n)!/n!/2^n; \\ == (2n-1)!!
s(n)=f(n) - sum(k=1, n-1, f(k)*s(n-k) )
a(n)=f(n)-s(n)
\\? for(n=0,22,print1(a(n),", "))
0, 0, 1, 5, 31, 239, 2233, 24725, 318631, 4707359, 78691633, 1471482725, 30469552111, 692488851599, 17141242421353, 459033875802485, 13221994489388791, 407574126219013439, 13386292717807416673, 466636446695213384645, 17205919477720642772671, 669019022588385113932079, 27357684052927560953626393,
cheers, jj
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