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%I #30 Aug 03 2014 14:01:36
%S 3,30,315,3780,51975,810810,14189175,275675400,5892561675,
%T 137493105750,3478575575475,94870242967500,2774954606799375,
%U 86663966950811250,2878481759437659375,101322557932205610000,3767932623103896121875,147614301587482048068750
%N Number of near-matchings on the complete graph over 2n+1 vertices.
%C A near-matching on the complete graph over 2n+1 vertices is an edge cover such that all but two edges are pairwise non-adjacent. A001147 corresponds to the number of matchings in even sized complete graphs.
%F a(n) = (2n+1)! / (2^n (n-1)!)
%t Table[(2*n + 1)!/(2^n (n - 1)!), {n, 30}] (* _T. D. Noe_, Nov 15 2011 *)
%Y Cf. A001147.
%K nonn
%O 1,1
%A _Ivo Vigan_, Nov 14 2011
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