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A053507 a(n) = binomial(n-1,2)*n^(n-3). 11
0, 0, 1, 12, 150, 2160, 36015, 688128, 14880348, 360000000, 9646149645, 283787919360, 9098660462034, 315866083233792, 11806916748046875, 472877960873902080, 20205339187128111480, 917543123840934346752, 44131536275846038655193 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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.

REFERENCES

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Prop. 5.3.2.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

FORMULA

E.g.f.: -1/3!*LambertW(-x)^3. - Vladeta Jovovic, Apr 07 2001

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 *)

PROG

(MAGMA) [Binomial(n-1, 2)*n^(n-3):n in [1..20]]; // Vincenzo Librandi, Sep 22 2011

(PARI) for(n=1, 25, print1(binomial(n-1, 2)*n^(n-3), ", ")) \\ G. C. Greubel, Jan 18 2017

CROSSREFS

Cf. A000169, A053506, A053508, A053509, A081133, A081132. Equals 2*A065513. A diagonal of A081130.

Sequence in context: A056345 A264233 A068768 * A060917 A113358 A293153

Adjacent sequences:  A053504 A053505 A053506 * A053508 A053509 A053510

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 2000

STATUS

approved

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Last modified October 23 05:50 EDT 2018. Contains 316519 sequences. (Running on oeis4.)