%I #6 Mar 08 2022 11:36:08
%S 0,1,3,3,30,15,315,105,3780,945,51975,10395,810810,135135,14189175,
%T 2027025,275675400,34459425,5892561675,654729075,137493105750,
%U 13749310575,3478575575475,316234143225,94870242967500,7905853580625,2774954606799375,213458046676875,86663966950811250,6190283353629375
%N Number of minimum edge covers of the complete graph K_n.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteGraph.html">Complete Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimumEdgeCover.html">Minimum Edge Cover</a>
%F a(n) = (n - 1)!! for n == 0 (mod 2).
%F a(n) = 2^((1 - n)/2)*n!/Gamma((n - 1)/2) for n == 1 (mod 2).
%F a(1) = 0, a(2) = 1, a(n) = (n - 1)*(((n - 2)*(n - 1)*n - 4)*a(n - 2) - 6*a(n - 1))/(n*(11 + (n - 6)*n) - 10).
%t Table[Piecewise[{{(2^((1 - n)/2) Gamma[n + 1])/Gamma[(n - 1)/2], Mod[n, 2] == 1}, {(n - 1)!!, Mod[n, 2] == 0}}, 0], {n, 20}]
%t RecurrenceTable[{a[1] == 0, a[2] == 1, a[n] == ((n - 1) (((n - 2) (n - 1) n - 4) a[n - 2] - 6 a[n - 1]))/(n (11 + (n - 6) n) - 10)}, a, {n, 20}]
%K nonn
%O 1,3
%A _Eric W. Weisstein_, Feb 27 2022