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A053507
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Binomial(n-1,2)*n^(n-3).
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7
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0, 0, 1, 12, 150, 2160, 36015, 688128, 14880348, 360000000, 9646149645, 283787919360, 9098660462034, 315866083233792, 11806916748046875, 472877960873902080, 20205339187128111480, 917543123840934346752, 44131536275846038655193
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Number of connected unicyclic simple graphs on n labeled nodes such that the unique cycle has length 3. - Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 27 2001
Each simple graph (of this type) corresponds to exactly two 'functional digraphs' counted by A065513.
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REFERENCES
| R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Prop. 5.3.2.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..100
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FORMULA
| E.g.f.: -1/3!*LambertW(-x)^3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 07 2001
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MATHEMATICA
| nn = 20; t = Sum[n^(n - 1) x^n/n!, {n, 1, nn}]; Drop[
Range[0, nn]! CoefficientList[Series[t^3/3!, {x, 0, nn}], x], 1] (*Geoffrey Critzer, Jan 22 2012*)
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PROG
| (MAGMA) [Binomial(n-1, 2)*n^(n-3):n in [1..20]]; // Vincenzo Librandi, Sep 22 2011
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CROSSREFS
| Cf. A000169, A053506-A053509, A081133, A081132. Equals 2*A065513. A diagonal of A081130.
Sequence in context: A056351 A056345 A068768 * A060917 A113358 A015611
Adjacent sequences: A053504 A053505 A053506 * A053508 A053509 A053510
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 15 2000
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