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A297527 Number of maximum matchings in the complete tripartite graph K_{n,n,n}.

%I A297527 #15 Feb 16 2025 08:33:52
%S A297527 3,8,324,1728,216000,1728000,444528000,4741632000,2073989836800,
%T A297527 27653197824000,18403203151872000,294451250429952000,
%U A297527 277246884511973376000,5175275177556836352000,6549957646595371008000000,139732429794034581504000000,228835142526030632976384000000
%N A297527 Number of maximum matchings in the complete tripartite graph K_{n,n,n}.
%C A297527 For even n, a maximum matching will be a perfect matching. For odd n there will be one unmatched vertex. - _Andrew Howroyd_, Jan 01 2018
%H A297527 Andrew Howroyd, <a href="/A297527/b297527.txt">Table of n, a(n) for n = 1..100</a>
%H A297527 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite Graph</a>
%H A297527 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Matching.html">Matching</a>
%H A297527 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximumIndependentEdgeSet.html">Maximum Independent Edge Set</a>
%F A297527 a(n) = binomial(n, floor(n/2))^3 * floor(n/2)! * ceiling(n/2)!^2 * (2-(-1)^n). - _Andrew Howroyd_, Jan 01 2018
%F A297527 -8*(n+2)*(9*n^2+34*n+30)*(n+1)^3*a(n)+12*(n+2)*(n^2+5*n+5)*a(n+1)+(n+3)*(9*n^2+16*n+5)*a(n+2) = 0. - _Eric W. Weisstein_, Jan 06 2018
%t A297527 Table[Binomial[n, Floor[n/2]]^3 Floor[n/2]! Ceiling[n/2]!^2 (2 - (-1)^n), {n, 20}]
%t A297527 RecurrenceTable[{-8 (1 + n)^3 (2 + n) (30 + 34 n + 9 n^2) a[n] + 12 (2 + n) (5 + 5 n + n^2) a[1 + n] + (3 + n) (5 + 16 n + 9 n^2) a[2 + n] == 0, a[1] == 3, a[2] == 8}, a[n], {n, 20}]
%o A297527 (PARI) a(n)={if(n%2==0, binomial(n,n/2)^3*(n/2)!^3, 3*binomial(n,(n-1)/2)^3*((n+1)/2)!^2*((n-1)/2)!)} \\ _Andrew Howroyd_, Jan 01 2018
%Y A297527 Cf. A293075, A297008, A297487.
%K A297527 nonn
%O A297527 1,1
%A A297527 _Eric W. Weisstein_, Dec 31 2017
%E A297527 Terms a(11) and beyond from _Andrew Howroyd_, Jan 01 2018