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A293075
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Number of matchings in the complete tripartite graph K_{n,n,n}.
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3
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4, 51, 1126, 37201, 1670136, 96502339, 6900041506, 593717817921, 60163621650316, 7059439676098291, 946047724677141054, 143165355635117094481, 24232437980331557100736, 4550485215254864673978051, 941387925046160753185319866, 213240954445118902597065224449
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OFFSET
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1,1
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LINKS
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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
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FORMULA
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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
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MATHEMATICA
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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}]
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PROG
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(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
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CROSSREFS
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Cf. A002720 (matchings in complete bipartite graph).
Sequence in context: A349653 A235325 A230401 * A300732 A220282 A235326
Adjacent sequences: A293072 A293073 A293074 * A293076 A293077 A293078
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KEYWORD
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nonn
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AUTHOR
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Eric W. Weisstein, Sep 30 2017
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EXTENSIONS
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Terms a(11) and beyond from Andrew Howroyd, Oct 02 2017
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STATUS
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approved
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