A297487 Number of maximal matchings in the complete tripartite graph K_{n,n,n}.

3, 14, 342, 5256, 252360, 7950960, 582346800, 30400755840, 3055726477440, 234650484230400, 30479146156166400, 3193083216360576000, 515174657767010841600, 69927761804930559129600, 13622234004598726450944000, 2307722078006148475736064000

Offset: 1

Author

Eric W. Weisstein, Dec 30 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100
• Eric Weisstein's World of Mathematics, Complete Tripartite Graph
• Eric Weisstein's World of Mathematics, Matching
• Eric Weisstein's World of Mathematics, Maximal Independent Edge Set

Crossrefs

Cf. A293075.

Programs

Mathematica

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}]

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

Extensions

Terms a(6) and beyond from Andrew Howroyd, Dec 30 2017