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 A097632 #27 Jan 16 2024 10:30:54
%S A097632 2,12,64,672,8448,138240,2672640,60641280,1568931840,45705461760,
%T A097632 1478924697600,52646746521600,2044394156851200,86005817907609600,
%U A097632 3896481847600742400,189139342470414336000,9793081532749971456000,538748376721309827072000,31381673358053118836736000
%N A097632 a(n) = 2^n * Lucas(n) * (n-1)!.
%C A097632 Number of possible well-colored cycles on n nodes. Well-colored means, each green vertex has at least a red child, each red vertex has no red child.
%H A097632 A.H.M. Smeets, <a href="/A097632/b097632.txt">Table of n, a(n) for n = 1..100</a>
%H A097632 C. Banderier, J.-M. Le Bars, and V. Ravelomanana, <a href="https://arxiv.org/abs/math/0411138">Generating functions for kernels of digraphs</a>, arXiv:math/0411138 [math.CO], 2004.
%F A097632 E.g.f.: -log(1-2*x-4*x^2).
%F A097632 a(n) = A000204(n) * A066318(n).
%F A097632 a(n) ~ sqrt(2*Pi/n)*(2*n*phi/e)^n. - _Stefano Spezia_, Jan 16 2024
%t A097632 a[n_] := 2^n*LucasL[n,1]*(n-1)!; Array[a,19] (* or *)
%t A097632 nmax=19; CoefficientList[Series[-Log[1-2x-4x^2], {x,0,nmax}], x]Range[0,nmax]! (* _Stefano Spezia_, Jan 15 2024 *)
%o A097632 (Python)
%o A097632 def A097632(n):
%o A097632 L0, L1, F, i = 1, 2, 2, 1
%o A097632 while i < n:
%o A097632 L0, L1, F, i = L0+L1, L0, 2*i*F, i+1
%o A097632 return L0*F # _A.H.M. Smeets_, Jan 15 2024
%Y A097632 Cf. A000079, A000142, A000204, A066318, A087131.
%K A097632 nonn
%O A097632 1,1
%A A097632 _Ralf Stephan_, Aug 17 2004
%E A097632 Definition corrected by and a(18)-a(19) from _Stefano Spezia_, Jan 15 2024