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%I #37 Apr 15 2021 20:23:40
%S 1,1,2,7,41,376,5177,103237,2922446,116011231,6433447397,498234407452,
%T 54007795331921,8213123246906761,1756336596363006842,
%U 528975889250504033527,224688018516023267969441,134708289561117007261966816
%N Number of labeled bipartite graphs with n nodes.
%D Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 406.
%D H. S. Wilf, Generatingfunctionology, Academic Press, NY, 1990, p. 80, Eq. 3.11.5.
%H T. D. Noe, <a href="/A047864/b047864.txt">Table of n, a(n) for n = 0..50</a>
%H Vladislav Bína, 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 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.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/n-ColorableGraph.html">n-Colorable Graph</a>
%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Bipartite, k-colorable and k-colored graphs</a>
%H 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]
%F E.g.f.: sqrt( e.g.f. for A047863 ).
%t 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 (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 Row sums of A117279.
%Y The unlabeled version is A033995.
%Y Cf. A001832.
%K nonn,nice,easy
%O 0,3
%A _N. J. A. Sloane_
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