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 A129583 #19 May 07 2021 20:28:27 %S A129583 1,1,0,0,12,312,13824,1147488,178672128,52666091712,29715982846848, %T A129583 32452221242518272,69259424722321036032,291060255757818125657088, %U A129583 2421848956937579216663491584,40050322614433939228627991906304,1319551659023608317386779165849208832 %N A129583 Number of labeled bi-point-determining graphs with n vertices. %C A129583 A bi-point determining graph is a graph in which no two vertices have the same neighborhoods or the same augmented neighborhoods (the augmented neighborhood of a vertex is the neighborhood of the vertex union the vertex itself). %D A129583 R. C. Read, The Enumeration of Mating-Type Graphs. Report CORR 89-38, Dept. Combinatorics and Optimization, Univ. Waterloo, 1989. %H A129583 Andrew Howroyd, <a href="/A129583/b129583.txt">Table of n, a(n) for n = 0..50</a> %H A129583 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 A129583 E.g.f.: G(2*log(1+x)-x) where G(x) is the e.g.f. of A006125. %o A129583 (PARI) seq(n)={my(g=sum(k=0, n, 2^binomial(k,2)*x^k/k!) + O(x*x^n)); Vec(serlaplace(subst(g, x, 2*log(1+x+O(x*x^n))-x)))} \\ _Andrew Howroyd_, May 06 2021 %Y A129583 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 A129583 nice,nonn %O A129583 0,5 %A A129583 Ji Li (vieplivee(AT)hotmail.com), May 07 2007 %E A129583 a(0)=1 prepended and terms a(13) and beyond from _Andrew Howroyd_, May 06 2021