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 A047864 #50 Feb 16 2025 08:32:39
%S A047864 1,1,2,7,41,376,5177,103237,2922446,116011231,6433447397,498234407452,
%T A047864 54007795331921,8213123246906761,1756336596363006842,
%U A047864 528975889250504033527,224688018516023267969441,134708289561117007261966816
%N A047864 Number of labeled bipartite graphs with n nodes.
%D A047864 Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 406.
%D A047864 H. S. Wilf, Generatingfunctionology, Academic Press, NY, 1990, p. 80, Eq. 3.11.5.
%H A047864 T. D. Noe, <a href="/A047864/b047864.txt">Table of n, a(n) for n = 0..50</a>
%H A047864 Vladislav Bína and Jiří Přibil, <a href="http://cmuc.karlin.mff.cuni.cz/cmuc1502/abs/binapri.pdf">Note on enumeration of labeled split graphs</a>, Comment. Math. Univ. Carolin. 56,2 (2015) 133-137.
%H A047864 S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Bipartite, k-colorable and k-colored graphs</a>. [Broken link]
%H A047864 S. R. Finch, <a href="/A191371/a191371.pdf">Bipartite, k-colorable and k-colored graphs</a>, June 5, 2003. [Cached copy, with permission of the author]
%H A047864 Qipeng Kuang, Ondřej Kuželka, Yuanhong Wang, and Yuyi Wang, <a href="https://arxiv.org/abs/2407.11877">Bridging Weighted First Order Model Counting and Graph Polynomials</a>, arXiv:2407.11877 [cs.LO], 2024. See p. 32.
%H A047864 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/n-ColorableGraph.html">n-Colorable Graph</a>.
%H A047864 H. S. Wilf, <a href="http://www.math.upenn.edu/~wilf/DownldGF.html">Generatingfunctionology</a>, 2nd edn., Academic Press, NY, 1994, p. 89, Eq. 3.11.5.
%F A047864 E.g.f.: sqrt( e.g.f. for A047863 ).
%t A047864 nn = 20; a = Sum[Sum[Binomial[n, k] 2^(k (n - k)), {k, 0, n}] x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[a^(1/2), {x, 0, nn}], x] (* _Geoffrey Critzer_, Jan 15 2012 *)
%o A047864 (PARI) N=18; x='x+O('x^N); Vec(serlaplace(sqrt(sum(n=0, N, exp(2^n*x)*x^n/n!)))) \\ _Gheorghe Coserea_, Nov 13 2017
%Y A047864 Row sums of A117279.
%Y A047864 The unlabeled version is A033995.
%Y A047864 Cf. A001832, A047863.
%K A047864 nonn,nice,easy
%O A047864 0,3
%A A047864 _N. J. A. Sloane_