Search: id:A104209
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%I A104209
%S A104209 1,3,39,819,23949,898947,41212155,2232057171,139455901101,
%T A104209 9873341493231,781184921112075,68309191570851759,
%U A104209 6541702440222052137,680922615974259589527,76544749927261960908807
%N A104209 Number of labeled directed multigraphs with n arrows and no vertex of 
               degree 0.
%C A104209 These are the dimensions of the homogeneous components of a commutative 
               graded Hopf algebra generalizing quasi-symmetric functions.
%D A104209 J.-C. Novelli, J.-Y. Thibon and N. M. Thiery, Algebres de Hopf de graphes, 
               C.R. Acad. Sci. Paris (Comptes Rendus Mathematique), 339 (2004), 
               607-610.
%F A104209 a(n) = sum{m=0..infinity, binomial(m^2+n-1, n)/2^(m+1)}
%F A104209 G.f.: sum{m=0..infinity, (1-x)^(-m^2)/2^(m+1)}. Row sums of A120945. 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 25 2006
%e A104209 a(1)=3, the three graphs being (1 ->2), (2 ->1) and (1 ->1).
%p A104209 d:=proc(n) local m;sum(binomial(m^2+n-1,n)/2^(m+1),m=0..infinity);end;
%t A104209 f[n_] := Sum[ Binomial[m^2 + n - 1, n]/2^(m + 1), {m, 0, Infinity}]; 
               Table[ f[n], {n, 0, 15}] (from Robert G. Wilson v Mar 16 2005)
%Y A104209 Cf. A052171 (counts same objects up to labeling).
%Y A104209 Cf. A020561.
%Y A104209 Sequence in context: A082954 A050392 A014850 this_sequence A121247 A064732 
               A092610
%Y A104209 Adjacent sequences: A104206 A104207 A104208 this_sequence A104210 A104211 
               A104212
%K A104209 nonn
%O A104209 1,2
%A A104209 Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Mar 13 2005
%E A104209 Corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 
               16 2005

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