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
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, 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