%I A005416 M4259
%S A005416 1,1,6,50,518,6354,89782,1435330,25625910,505785122,10944711398,
%T A005416 257834384850,6572585595622,180334118225650,5300553714899094,166206234856979810,
%U A005416 5538980473666776854,195527829569946627138,7288988096561232432070
%N A005416 Vertex diagrams of order 2n.
%D A005416 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005416 P. Cvitanovic, Asymptotic estimates and gauge invariance, Nuclear Phys. 
               B 127 (1977), 176-188.
%H A005416 T. D. Noe, <a href="b005416.txt">Table of n, a(n) for n=0..100</a>
%H A005416 D. J. Broadhurst, <a href="http://arXiv.org/abs/hep-ph/9909336">Four-loop 
               Dyson-Schwinger-Johnson anatomy</a>
%F A005416 Let s_n=(2n)!/(2^n*n!) (A001147), S(x)=Sum_{n >= 0} s_n*x^n; sequence 
               has g.f. A(x) satisfying 1-1/S(x)=x*A(x)*S(x).
%o A005416 (PARI) {a(n)=local(A); if(n<0, 0, A=sum(k=0, n+1, (2*k)!/k!/2^k*x^k, 
               x^2*O(x^n)); polcoeff( (A-1)/(x*A^2), n))} /* Michael Somos Oct 11 
               2006 */
%Y A005416 Cf. A049464.
%Y A005416 Sequence in context: A090409 A039742 A125558 this_sequence A105617 A094072 
               A058784
%Y A005416 Adjacent sequences: A005413 A005414 A005415 this_sequence A005417 A005418 
               A005419
%K A005416 nonn,nice,easy
%O A005416 0,3
%A A005416 N. J. A. Sloane (njas(AT)research.att.com).