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

1,4

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

Mathematica

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 *)

Prog

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

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

Extensions

Incorrect Mathematica program deleted by Harvey P. Dale, Sep 24 2019

Status

approved