This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053507 #43 Jun 23 2025 09:59:00
%S A053507 0,0,1,12,150,2160,36015,688128,14880348,360000000,9646149645,
%T A053507 283787919360,9098660462034,315866083233792,11806916748046875,
%U A053507 472877960873902080,20205339187128111480,917543123840934346752,44131536275846038655193
%N A053507 a(n) = binomial(n-1,2)*n^(n-3).
%C A053507 Number of connected unicyclic simple graphs on n labeled nodes such that the unique cycle has length 3. - _Len Smiley_, Nov 27 2001
%C A053507 Each simple graph (of this type) corresponds to exactly two 'functional digraphs' counted by A065513.
%D A053507 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Prop. 5.3.2.
%H A053507 Vincenzo Librandi, <a href="/A053507/b053507.txt">Table of n, a(n) for n = 1..100</a>
%F A053507 E.g.f.: -LambertW(-x)^3/3!. - _Vladeta Jovovic_, Apr 07 2001
%t A053507 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 *)
%t A053507 Table[Binomial[n-1,2]n^(n-3),{n,20}] (* _Harvey P. Dale_, Sep 24 2019 *)
%o A053507 (Magma) [Binomial(n-1,2)*n^(n-3):n in [1..20]]; // _Vincenzo Librandi_, Sep 22 2011
%o A053507 (PARI) vector(20, n, binomial(n-1,2)*n^(n-3)) \\ _G. C. Greubel_, Jan 18 2017
%o A053507 (Magma) [Binomial(n-1,2)*n^(n-3): n in [1..20]]; // _G. C. Greubel_, May 15 2019
%o A053507 (Sage) [binomial(n-1,2)*n^(n-3) for n in (1..20)] # _G. C. Greubel_, May 15 2019
%o A053507 (GAP) List([1..20], n-> Binomial(n-1,2)*n^(n-3)); # _G. C. Greubel_, May 15 2019
%Y A053507 Cf. A000169, A053506, A053508, A053509, A081133, A081132.
%Y A053507 Equals 2*A065513. A diagonal of A081130.
%K A053507 nonn,easy
%O A053507 1,4
%A A053507 _N. J. A. Sloane_, Jan 15 2000