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

1,1

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

Formula

From Vaclav Kotesovec, Feb 06 2026: (Start)

Recurrence: (8*n^5 - 164*n^4 + 1270*n^3 - 4543*n^2 + 7500*n - 4572)*a(n) = - (8*n^7 - 188*n^6 + 1850*n^5 - 9669*n^4 + 28259*n^3 - 45091*n^2 + 35160*n - 9612)*a(n-1) + (144*n^8 - 3440*n^7 + 33608*n^6 - 173708*n^5 + 520473*n^4 - 929162*n^3 + 966517*n^2 - 532860*n + 116964)*a(n-2) + 8*(n-2)^2*(16*n^8 - 400*n^7 + 4252*n^6 - 24816*n^5 + 86024*n^4 - 179519*n^3 + 217466*n^2 - 136875*n + 32751)*a(n-3) - 8*(n-3)^3*(n-2)^2*(80*n^6 - 1616*n^5 + 12536*n^4 - 46276*n^3 + 84401*n^2 - 70686*n + 20097)*a(n-4) - 64*(n-4)^3*(n-3)^3*(n-2)^2*(8*n^5 - 124*n^4 + 694*n^3 - 1637*n^2 + 1608*n - 501)*a(n-5).

a(n) ~ 3 * 2^((3*n+1)/2) * exp(sqrt(n/2) - 3*n/2 - 3/8) * n^(3*n/2). (End)

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}]

Prog

(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

Crossrefs

Cf. A293075.

Sequence in context: A144985 A168590 A309028 * A297484 A289878 A081397

Adjacent sequences: A297484 A297485 A297486 * A297488 A297489 A297490

Keyword

nonn

Author

Eric W. Weisstein, Dec 30 2017

Extensions

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

Status

approved