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, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching
FORMULA
a(n) = Sum_{i,j,k} binomial(n, i)^2 * binomial(n, j) * binomial(n-i, j) * binomial(n-i, k) * binomial(n-j, k) * i!*j!*k!. - Andrew Howroyd, Oct 02 2017
MATHEMATICA
Table[Sum[Binomial[n, i]^2 Binomial[n, j] Binomial[n - i, j] Binomial[n - i, k] Binomial[n - j, k] i! j! k!, {i, 0, n}, {j, 0, n - i}, {k, 0, Min[n - i, n - j]}], {n, 20}]
Table[Sum[(-1)^(i - n) Binomial[n, i]^2 Binomial[n, j] Binomial[-i + n, j] i! j! HypergeometricU[i - n, 1 + i - j, -1], {i, 0, n}, {j, 0, n - i}], {n, 20}]
PROG
(PARI) a(n) = sum(i=0, n, sum(j=0, n-i, sum(k=0, min(n-i, n-j), binomial(n, i)^2 * binomial(n, j) * binomial(n-i, j) * binomial(n-i, k) * binomial(n-j, k) * i!*j!*k!))); \\ Andrew Howroyd, Oct 02 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Sep 30 2017
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Oct 02 2017
STATUS
approved