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a(n) = binomial(n-1,2)*n^(n-3).
15

%I #34 Sep 08 2022 08:45:00

%S 0,0,1,12,150,2160,36015,688128,14880348,360000000,9646149645,

%T 283787919360,9098660462034,315866083233792,11806916748046875,

%U 472877960873902080,20205339187128111480,917543123840934346752,44131536275846038655193

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

%C Number of connected unicyclic simple graphs on n labeled nodes such that the unique cycle has length 3. - _Len Smiley_, Nov 27 2001

%C Each simple graph (of this type) corresponds to exactly two 'functional digraphs' counted by A065513.

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

%H Vincenzo Librandi, <a href="/A053507/b053507.txt">Table of n, a(n) for n = 1..100</a>

%F E.g.f.: -LambertW(-x)^3/3!. - _Vladeta Jovovic_, Apr 07 2001

%t Range[0, nn]! CoefficientList[Series[t^3/3!, {x, 0, nn}], x], 1] (* _Geoffrey Critzer_, Jan 22 2012 *)

%t Table[Binomial[n-1,2]n^(n-3),{n,20}] (* _Harvey P. Dale_, Sep 24 2019 *)

%o (Magma) [Binomial(n-1,2)*n^(n-3):n in [1..20]]; // _Vincenzo Librandi_, Sep 22 2011

%o (PARI) vector(20, n, binomial(n-1,2)*n^(n-3)) \\ _G. C. Greubel_, Jan 18 2017

%o (Magma) [Binomial(n-1,2)*n^(n-3): n in [1..20]]; // _G. C. Greubel_, May 15 2019

%o (Sage) [binomial(n-1,2)*n^(n-3) for n in (1..20)] # _G. C. Greubel_, May 15 2019

%o (GAP) List([1..20], n-> Binomial(n-1,2)*n^(n-3)) # _G. C. Greubel_, May 15 2019

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

%Y Equals 2*A065513. A diagonal of A081130.

%K nonn

%O 1,4

%A _N. J. A. Sloane_, Jan 15 2000

%E Incorrect Mathematica program deleted by _Harvey P. Dale_, Sep 24 2019