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 A119913 #14 Feb 16 2025 08:33:01
%S A119913 0,0,2,14,74,394,2344,16036,125628,1112028,10976118,119481218,
%T A119913 1421542550,18348340022,255323504812,3809950976872,60683990530072,
%U A119913 1027542662934744,18430998766219146,349096664728623126,6962409983976703106,145841989688186383106
%N A119913 Number of directed simple cycles in the complete graph K_n.
%C A119913 That is, the number of subsets of at least 3 elements out of n, ordered up to cyclic permutations.
%C A119913 For n > 2, also the number of undirected cycles in the n-barbell graph. - _Eric W. Weisstein_, Dec 14 2017
%H A119913 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarbellGraph.html">Barbell Graph</a>
%H A119913 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteGraph.html">Complete Graph</a>
%H A119913 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%F A119913 a(n) = Sum_{k=3..n} C(n,k) * (k-1)!.
%F A119913 a(n) = Sum_{i=2..n-1} (floor(e*i!)) - (n+3)(n-2)/2.
%F A119913 a(n) = Sum_{k=1..n-1} A038154(k).
%F A119913 a(n) = 2*A002807(n). - _Vladeta Jovovic_, Aug 04 2006
%e A119913 a(4)=14 because there are 6 4-cycles and 8 3-cycles.
%t A119913 Table[n (2 HypergeometricPFQ[{1, 1, 1 - n}, {2}, -1] - n - 1)/2, {n, 20}] (* _Eric W. Weisstein_, Dec 14 2017 *)
%o A119913 (MATLAB) function a = an(n) s = 0; for i = 2:n-1 s = s+fix(exp(1)*factorial(i)); end a = s - (n+3)*(n-2)/2;
%Y A119913 Cf. A038154.
%Y A119913 Cf. A002807 (number of undirected cycles).
%K A119913 nonn
%O A119913 1,3
%A A119913 Amir M. Ben-Amram (amirben(AT)mta.ac.il), Aug 02 2006
%E A119913 More terms from _Max Alekseyev_, Jan 18 2012