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A239910
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Number of forests with three connected components in the complete graph K_{n}.
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5
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0, 0, 1, 6, 45, 435, 5250, 76608, 1316574, 26100000, 587030895, 14780620800, 412069511139, 12604714327296, 419801484375000, 15123782440058880, 586049426860524300, 24307340986526810112, 1074495780444130114509, 50429952000000000000000
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OFFSET
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1,4
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COMMENTS
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Equation (47) of Liu-Chow (1984) also gives the analogous formulas for four and five components. (They should also be entered into the OEIS, in case someone wants to help.)
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LINKS
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FORMULA
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a(n) = n^(n-6)*(n-1)*(n-2)*(n^2+13*n+60)/8.
E.g.f.: T(x)^{3}/3!, where T(x) is the e.g.f. for the number of spanning trees in K_{n} A000272, i.e., T(x) = Sum_{i>=1} i^(i-2)*x^i/i!. (End)
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MAPLE
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f := n-> (n-1)*(n-2)*n^(n-6)*(n^2+13*n+60)/8; [seq(f(n), n=3..20)];
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MATHEMATICA
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PROG
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(Magma) [(n-1)*(n-2)*n^(n-6)*(n^2+13*n+60)/8: n in [1..20]]; // Vincenzo Librandi, Apr 10 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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