%I A000273 M3032 N1229
%S A000273 1,1,3,16,218,9608,1540944,882033440,1793359192848,13027956824399552,
%T A000273 341260431952972580352,32522909385055886111197440,
%U A000273 11366745430825400574433894004224
%N A000273 Number of directed graphs (or digraphs) with n nodes.
%D A000273 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000273 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000273 CRC Handbook of Combinatorial Designs, 1996, p. 651.
%D A000273 R. L. Davies, The numbers of structures of finite relations, Proc. Amer. 
               Math. Soc., 4 (1953), 486-494.
%D A000273 F. Harary, Graph Theory. Addison-Wesley, Reading, MA, 1969, p. 225.
%D A000273 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 124, Table 5.1.2 and p. 241, Table A4.
%D A000273 M. D. McIlroy, Calculation of numbers of structures of relations on finite 
               sets, Massachusetts Institute of Technology, Research Laboratory 
               of Electronics, Quarterly Progress Reports, No. 17, Sept. 15, 1955, 
               pp. 14-22.
%D A000273 W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. 
               Ann., 174 (1967), 53-78.
%D A000273 J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 
               2004; p. 522.
%H A000273 Keith Briggs, <a href="b000273.txt">Table of n, a(n) for n = 0..64</a>
%H A000273 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A000273 G. Pfeiffer, <a href="http://www.cs.uwaterloo.ca/journals/JIS/">Counting 
               Transitive Relations</a>, Journal of Integer Sequences, Vol. 7 (2004), 
               Article 04.3.2.
%H A000273 L. Travis, <a href="http://arXiv.org/abs/math.CO/9811127">[math/9811127] 
               Graphical Enumeration: A Species-Theoretic Approach</a>
%H A000273 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DirectedGraph.html">Link to a section of The World of Mathematics.</
               a>
%H A000273 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%p A000273 (Maple code from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 06 2006) 
               with(combinat):with(numtheory):
%p A000273 for n from 1 to 20 do p:=partition(n):
%p A000273 s:=0:for k from 1 to nops(p) do
%p A000273 q:=convert(p[k],multiset):
%p A000273 for i from 1 to n do a(i):=0:od:for i from 1 to nops(q) do a(q[i][1]):=q[i][2]:od:
%p A000273 c:=1:ord:=1:for i from 1 to n do c:=c*a(i)!*i^a(i): if a(i)<>0 then ord:=lcm(ord,
               i):fi:od:
%p A000273 g:=0:for d from 1 to ord do if ord mod d=0 then g1:=0:for del from 1 
               to d do if del<=n and d mod del=0 then g1:=g1+del*a(del):fi:od:g:=g+phi(ord/
               d)*g1*(g1-1):fi:od:
%p A000273 s:=s+2^(g/ord)/c:
%p A000273 od:
%p A000273 print(n,s):
%p A000273 od:
%Y A000273 Sequence in context: A007006 A166860 A113597 this_sequence A071897 A013923 
               A053466
%Y A000273 Adjacent sequences: A000270 A000271 A000272 this_sequence A000274 A000275 
               A000276
%K A000273 nonn,core,nice,easy
%O A000273 0,3
%A A000273 N. J. A. Sloane (njas(AT)research.att.com).
%E A000273 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 14 1999