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 A202081 #20 Feb 17 2025 03:15:38
%S A202081 1,1,2,8,46,298,2206,19009,187076,2053349,24800484,327067043,
%T A202081 4677505768,72075818159,1189985755128,20952274850927,391829421176768,
%U A202081 7755079821666945,161926610838369418,3556807008080385549,81979632030102053376,1978135038931568355707
%N A202081 The number of simple labeled graphs on n nodes whose connected components are cycles, stars, wheels, or paths.
%C A202081 Here a cycle is of length 3 or more, a star has at least 4 (total) vertices, a wheel has at least 4 (total) vertices, and a path can be an isolated vertex.
%D A202081 R. P. Stanley, Enumerative Combinatorics Volume 2, Cambridge 1999, problem 5.15
%H A202081 G. C. Greubel, <a href="/A202081/b202081.txt">Table of n, a(n) for n = 0..440</a>
%F A202081 E.g.f.: exp(x/2+x/(2*(1-x))) * exp(-x^2/2-x^3/4-x^4/8)/(1-x)^(x/2) * exp(-x-x^2-x^3/2 + x*exp(x)) * exp(-x/2-x^2/4)/(1-x)^(1/2). [corrected by _Jason Yuen_, Feb 17 2025]
%t A202081 nn = 16; a = x/(2 (1 - x)) + x/2; b = x^4/4! + Sum[(n (n - 2)!/2) x^n/n!, {n, 5, nn}]; c = x Exp[x] - x^3/2 - x^2 - x; d = -x/2 - x^2/4; Range[0, nn]! CoefficientList[Series[Exp[a]*Exp[b]*Exp[c]*Exp[d]/(1 - x)^(1/2), {x, 0, nn}], x]
%Y A202081 Cf. A001205, A053530, A053531, A011800.
%K A202081 nonn
%O A202081 0,3
%A A202081 _Geoffrey Critzer_, Dec 10 2011