Search: id:A005155
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%I A005155 M1886
%S A005155 1,1,2,8,54,533,6944,111850,2135740,47003045,1168832808,32363244260,
%T A005155 986532609608,32810811179569,1181865951824800,45823912079507918,
%U A005155 1902469319507438352,84195282530581058825,3956365033583165905568
%N A005155 Number of degree sequences of n-node graphs.
%C A005155 Given a simple graph, the degree sequence maps each vertex to the valence 
               or degree of that vertex.
%D A005155 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005155 R. P. Stanley, ``A zonotope associated with graphical degree sequences,
               '' in Applied Geometry and Discrete Combinatorics. DIMACS Series 
               in Discrete Math., Amer. Math. Soc., Vol. 4, pp. 555-570, 1991.
%D A005155 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Problem 5.16.
%D A005155 R. Simion, "Convex Polytopes and Enumeration", Adv. in Appl. Math. 18 
               (1997) pp. 149-180. See p. 161
%F A005155 There is an explicit formula and e.g.f.
%F A005155 E.g.f.: (sqrt((1-LambertW(-x))/(1+LambertW(-x)))-LambertW(-x)/x)*exp(-LambertW(-x)^2/
               2)/2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 21 2007
%o A005155 (PARI) {a(n)=local(A,B,C); if(n<0, 0, A=sum(k=1,n,k^k*x^k/k!,x*O(x^n)); 
               B=intformal(1+A); C=intformal(1/(1-B)); n!*polcoeff( (1+(1-B)*sqrt(1+2*A))/
               2*exp(C), n))} /* Michael Somos Aug 19 2005 */
%Y A005155 Cf. A004251 for graphs up to isomorphism.
%Y A005155 Sequence in context: A052599 A052662 A073564 this_sequence A005440 A139016 
               A134954
%Y A005155 Adjacent sequences: A005152 A005153 A005154 this_sequence A005156 A005157 
               A005158
%K A005155 nonn,nice,easy
%O A005155 0,3
%A A005155 N. J. A. Sloane (njas(AT)research.att.com).

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