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 A129585 #21 May 07 2021 15:45:09
%S A129585 1,1,0,0,12,252,12312,1061304,170176656,51134075424,29204599254624,
%T A129585 32130964585236096,68873851786953047040,290164895151435531345024,
%U A129585 2417786648013402212500060416,40014055814155246577685250570752,1318911434129029730677931158374449664
%N A129585 Number of labeled connected bi-point-determining graphs with n vertices (see A129583).
%C A129585 The calculation of connected bi-point-determining graphs is carried out by examining the connected components of bi-point-determining graphs. For more details, see reference.
%H A129585 Andrew Howroyd, <a href="/A129585/b129585.txt">Table of n, a(n) for n = 0..50</a>
%H A129585 Ira M. Gessel and Ji Li, <a href="https://doi.org/10.1016/j.jcta.2010.03.009">Enumeration of point-determining Graphs</a>, Journal of Combinatorial Theory, Series A 118 (2011) 591-612.
%F A129585 E.g.f.: 1 + x + log((Sum_{n>=0} 2^binomial(n,2)*(2*log(1+x)-x)^n/n!)/(1+x)). - Goran Kilibarda, _Vladeta Jovovic_, May 09 2007
%F A129585 E.g.f.: 1 + x + log(B(x)/(1+x)) where B(x) is the e.g.f. of A129583. - _Andrew Howroyd_, May 06 2021
%t A129585 max = 15; f[x_] := x + Log[ Sum[ 2^Binomial[n, 2]*((2*Log[1 + x] - x)^n/n!), {n, 0, max}]/(1 + x)]; A129585 = Drop[ CoefficientList[ Series[ f[x], {x, 0, max}], x]*Range[0, max]!, 1](* _Jean-François Alcover_, Jan 13 2012, after e.g.f. *)
%o A129585 (PARI) seq(n)={my(g=sum(k=0, n, 2^binomial(k,2)*x^k/k!) + O(x*x^n)); Vec(serlaplace(1+x+log(subst(g, x, 2*log(1+x+O(x*x^n))-x)/(1+x))))} \\ _Andrew Howroyd_, May 06 2021
%Y A129585 Cf. graphs: labeled A006125, unlabeled A000568; connected graphs: labeled A001187, unlabeled A001349; point-determining graphs: labeled A006024, unlabeled A004110; connected point-determining graphs: labeled A092430, unlabeled A004108; connected co-point-determining graphs: labeled A079306, unlabeled A004108; bi-point-determining graphs: labeled A129583, unlabeled A129584; connected bi-point-determining graphs: labeled A129585, unlabeled A129586; phylogenetic trees: labeled A000311, unlabeled A000669.
%K A129585 nice,nonn
%O A129585 0,5
%A A129585 Ji Li (vieplivee(AT)hotmail.com), May 07 2007
%E A129585 More terms from Goran Kilibarda, _Vladeta Jovovic_, May 09 2007
%E A129585 a(0)=1 prepended and terms a(16) and beyond from _Andrew Howroyd_, May 06 2021