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A297527
Number of maximum matchings in the complete tripartite graph K_{n,n,n}.
1
3, 8, 324, 1728, 216000, 1728000, 444528000, 4741632000, 2073989836800, 27653197824000, 18403203151872000, 294451250429952000, 277246884511973376000, 5175275177556836352000, 6549957646595371008000000, 139732429794034581504000000, 228835142526030632976384000000
OFFSET
1,1
COMMENTS
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
LINKS
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximum Independent Edge Set
FORMULA
a(n) = binomial(n, floor(n/2))^3 * floor(n/2)! * ceiling(n/2)!^2 * (2-(-1)^n). - Andrew Howroyd, Jan 01 2018
-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
MATHEMATICA
Table[Binomial[n, Floor[n/2]]^3 Floor[n/2]! Ceiling[n/2]!^2 (2 - (-1)^n), {n, 20}]
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}]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Dec 31 2017
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Jan 01 2018
STATUS
approved