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A053507
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a(n) = binomial(n-1,2)*n^(n-3).
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15
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0, 0, 1, 12, 150, 2160, 36015, 688128, 14880348, 360000000, 9646149645, 283787919360, 9098660462034, 315866083233792, 11806916748046875, 472877960873902080, 20205339187128111480, 917543123840934346752, 44131536275846038655193
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OFFSET
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1,4
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COMMENTS
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Number of connected unicyclic simple graphs on n labeled nodes such that the unique cycle has length 3. - Len Smiley, Nov 27 2001
Each simple graph (of this type) corresponds to exactly two 'functional digraphs' counted by A065513.
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REFERENCES
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R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Prop. 5.3.2.
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LINKS
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FORMULA
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MATHEMATICA
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Range[0, nn]! CoefficientList[Series[t^3/3!, {x, 0, nn}], x], 1] (* Geoffrey Critzer, Jan 22 2012 *)
Table[Binomial[n-1, 2]n^(n-3), {n, 20}] (* Harvey P. Dale, Sep 24 2019 *)
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PROG
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(PARI) vector(20, n, binomial(n-1, 2)*n^(n-3)) \\ G. C. Greubel, Jan 18 2017
(Magma) [Binomial(n-1, 2)*n^(n-3): n in [1..20]]; // G. C. Greubel, May 15 2019
(Sage) [binomial(n-1, 2)*n^(n-3) for n in (1..20)] # G. C. Greubel, May 15 2019
(GAP) List([1..20], n-> Binomial(n-1, 2)*n^(n-3)) # G. C. Greubel, May 15 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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