A053507 a(n) = binomial(n-1,2)*n^(n-3).

0, 0, 1, 12, 150, 2160, 36015, 688128, 14880348, 360000000, 9646149645, 283787919360, 9098660462034, 315866083233792, 11806916748046875, 472877960873902080, 20205339187128111480, 917543123840934346752, 44131536275846038655193

Offset: 1

Author

N. J. A. Sloane, Jan 15 2000

Keywords

• nonn
• easy

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

Crossrefs

Cf. A000169, A053506, A053508, A053509, A081133, A081132.

Equals 2*A065513. A diagonal of A081130.

Programs

GAP

List([1..20], n-> Binomial(n-1,2)*n^(n-3)); # G. C. Greubel, May 15 2019

Magma

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

Magma

[Binomial(n-1,2)*n^(n-3): n in [1..20]]; // G. C. Greubel, May 15 2019

Mathematica

nn = 20; t = Sum[n^(n - 1) x^n/n!, {n, 1, nn}]; Rest[Range[0, nn]! CoefficientList[Series[t^3/3!, {x, 0, nn}], x]] (* Geoffrey Critzer, Jan 22 2012 *)
Table[Binomial[n-1,2]n^(n-3),{n,20}] (* Harvey P. Dale, Sep 24 2019 *)

PARI

vector(20, n, binomial(n-1,2)*n^(n-3)) \\ G. C. Greubel, Jan 18 2017

Sage

[binomial(n-1,2)*n^(n-3) for n in (1..20)] # G. C. Greubel, May 15 2019

Formula

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