%I A003049 M3344
%S A003049 1,0,1,1,4,8,37,184,1782,31026,1148626,86539128,12798435868,
%T A003049 3620169692289,1940367005824561,1965937435288738165,
%U A003049 3766548132138130650270,13666503289976224080346733
%N A003049 Number of connected Eulerian graphs with n nodes.
%D A003049 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003049 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 117.
%D A003049 Valery A. Liskovets, Enumeration of Euler graphs. (Russian), Vesci Akad. 
               Navuk BSSR, Ser. Fiz.-Mat. Navuk 1970, No.6, 38-46 (1970). Math. 
               Rev., Vol. 44, 1972, p. 1195, #6557.
%D A003049 R. W. Robinson, Enumeration of Euler graphs, pp. 147-153 of F. Harary, 
               editor, Proof Techniques in Graph Theory. Academic Press, NY, 1969.
%D A003049 R. W. Robinson, personal communication.
%D A003049 R. W. Robinson, Numerical implementation of graph counting algorithms, 
               AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1979.
%H A003049 R. W. Robinson, <a href="b003049.txt">Table of n, a(n) for n = 1..26</
               a>
%H A003049 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 A003049 Erich Friedman, <a href="a003049.gif">Illustration of initial terms</
               a>
%H A003049 Brendan McKay, <a href="http://cs.anu.edu.au/~bdm/data/">Combinatorial 
               Data (Eulerian graphs)</a>
%H A003049 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EulerianGraph.html">Link to a section of The World of Mathematics.</
               a>
%F A003049 Let B(x) = g.f. for A002854. Then g.f. A(x) for A003049 satisfies 1+B(x) 
               = exp( Sum_{n=1..inf} A(x^n)/n) - Robinson (1969).
%F A003049 Inverse Euler transform of A002854. (This is equivalent to the Robinson 
               formula.) - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 24 
               2006
%Y A003049 Cf. A002854.
%Y A003049 Sequence in context: A100214 A047710 A063580 this_sequence A098563 A032301 
               A032213
%Y A003049 Adjacent sequences: A003046 A003047 A003048 this_sequence A003050 A003051 
               A003052
%K A003049 nonn,nice,easy
%O A003049 1,5
%A A003049 N. J. A. Sloane (njas(AT)research.att.com).
%E A003049 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 18 2000