A297487 - OEIS

%I #11 Jan 01 2018 11:54:29

%S 3,14,342,5256,252360,7950960,582346800,30400755840,3055726477440,

%T 234650484230400,30479146156166400,3193083216360576000,

%U 515174657767010841600,69927761804930559129600,13622234004598726450944000,2307722078006148475736064000

%N Number of maximal matchings in the complete tripartite graph K_n,n,n.

%H Andrew Howroyd, <a href="/A297487/b297487.txt">Table of n, a(n) for n = 1..100</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matching.html">Matching</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIndependentEdgeSet.html">Maximal Independent Edge Set</a>

%t Table[3 n! HypergeometricPFQ[{(1 - n)/2, -n, -n/2}, {1}, -4] - If[Mod[n, 2] == 0, 2 (n!/(n/2)!)^3, 0], {n, 20}]

%o (PARI) a(n)={if(n%2==0, binomial(n, n/2)*(n/2)!, 0)^3 + sum(k=0, (n-1)\2, 3*binomial(n, k)^2*binomial(n, 2*k)*binomial(2*k, k)*k!^2*(n-k)!)} \\ _Andrew Howroyd_, Dec 30 2017

%Y Cf. A293075.

%K nonn

%O 1,1

%A _Eric W. Weisstein_, Dec 30 2017

%E Terms a(6) and beyond from _Andrew Howroyd_, Dec 30 2017