A293075 Number of matchings in the complete tripartite graph K_{n,n,n}.

4, 51, 1126, 37201, 1670136, 96502339, 6900041506, 593717817921, 60163621650316, 7059439676098291, 946047724677141054, 143165355635117094481, 24232437980331557100736, 4550485215254864673978051, 941387925046160753185319866, 213240954445118902597065224449

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

Cf. A002720 (matchings in complete bipartite graph).

Sequence in context: A349653 A235325 A230401 * A300732 A220282 A235326

Adjacent sequences: A293072 A293073 A293074 * A293076 A293077 A293078

Keyword

nonn

Author

Eric W. Weisstein, Sep 30 2017

Extensions

Terms a(11) and beyond from Andrew Howroyd, Oct 02 2017

Status

approved