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 A006184 M3100 #29 Feb 16 2025 08:32:29
%S A006184 0,0,0,0,0,3,23,153,1077,8490,75234,742710,8084990,96192405,
%T A006184 1241588865,17277139383,257810397243,4106342523108,69531388662932,
%U A006184 1247182219179900,23622547999002444,471129863595453495,9868783491120925755,216617163296681315685,4971829898824570284305,119096935551493905531438,2972224576868227286710038,77153543251103295197353938
%N A006184 Number of cycles in the complement of a path.
%C A006184 Number of cycles in K_n - P_n. - _Sean A. Irvine_, Jan 17 2017
%D A006184 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006184 Andrew Howroyd, <a href="/A006184/b006184.txt">Table of n, a(n) for n = 0..200</a>
%H A006184 F. C. Holroyd and W. J. G. Wingate, <a href="http://dx.doi.org/10.1016/S0012-365X(85)80003-0">Cycles in the complement of a tree or other graph</a>, Discrete Math., 55 (1985), 267-282.
%H A006184 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A006184 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PathComplementGraph.html">Path Complement Graph</a>
%F A006184 a(n) = (1/2)*Sum_{k=3..n} Sum_{i=1..k} Sum_{j=0..k-i} (-1)^(k-i)*(i-1)!*2^j*binomial(n+i-k, i)*binomial(i, j)*binomial(k-i-1, k-i-j). - _Andrew Howroyd_, Apr 21 2018
%F A006184 a(n) ~ (n-1)! / (2*exp(1)). - _Vaclav Kotesovec_, Apr 22 2018
%t A006184 Array[(1/2)Sum[Sum[Sum[(-1)^(k - i) (i - 1)!*2^j*Binomial[# + i - k, i] Binomial[i, j] Binomial[k - i - 1, k - i - j], {j, 0, k - i}], {i, k}], {k, 3, #}] &, 28, 0] (* _Michael De Vlieger_, Apr 21 2018 *)
%t A006184 Table[Sum[(-1)^(k - i) Gamma[i] 2^j Binomial[n + i - k, i] Binomial[i, j] Binomial[k - i - 1, k - i - j], {k, 3, n}, {i, k}, {j, 0, k - i}]/2, {n, 20}] (* _Eric W. Weisstein_, Apr 23 2018 *)
%o A006184 (PARI) a(n)={sum(k=3, n, sum(i=1, k, sum(j=0, min(i,k-i), (-1)^(k-i)*(i-1)!*2^j*binomial(n+i-k, i)*binomial(i, j)*binomial(k-i-1, k-i-j))))/2} \\ _Andrew Howroyd_, Apr 21 2018
%Y A006184 Cf. A302734.
%K A006184 nonn
%O A006184 0,6
%A A006184 _N. J. A. Sloane_
%E A006184 a(0)-a(3) prepended, a(4) corrected, and more terms from _Sean A. Irvine_, Jan 17 2017