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A239910 Number of forests with three connected components in the complete graph K_{n}. 5
0, 0, 1, 6, 45, 435, 5250, 76608, 1316574, 26100000, 587030895, 14780620800, 412069511139, 12604714327296, 419801484375000, 15123782440058880, 586049426860524300, 24307340986526810112, 1074495780444130114509, 50429952000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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.)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

C. J. Liu and Yutze Chow, On operator and formal sum methods for graph enumeration problems, SIAM J. Algebraic Discrete Methods, 5 (1984), no. 3, 384--406. MR0752043 (86d:05059).

MAPLE

f := n-> (n-1)!*n^(n-6)*(n^2+13*n+60)/(8*(n-3)!); [seq(f(n), n=3..20)];

MATHEMATICA

Table[(n-1)*(n-2) * n^(n - 6) * (n^2 + 13 n + 60)/8, {n, 1, 20}] (* Vincenzo Librandi, Apr 10 2014, simplified by Vaclav Kotesovec, Feb 20 2020 *)

PROG

(MAGMA) [0, 0] cat [Factorial(n-1)*n^(n-6)*(n^2+13*n+60)/ (8*Factorial(n-3)): n in [3..20]]; // Vincenzo Librandi, Apr 10 2014

CROSSREFS

Cf. A000272, A083483.

Column m=3 of A105599. A diagonal of A138464. - Alois P. Heinz, Apr 10 2014

Sequence in context: A001879 A019577 A097814 * A228194 A331726 A084064

Adjacent sequences:  A239907 A239908 A239909 * A239911 A239912 A239913

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 09 2014

STATUS

approved

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Last modified September 18 16:05 EDT 2020. Contains 337169 sequences. (Running on oeis4.)