%I A000699 M3618 N1468
%S A000699 1,1,4,27,248,2830,38232,593859,10401712,202601898,4342263000,
%T A000699 101551822350,2573779506192,70282204726396,2057490936366320,
%U A000699 64291032462761955,2136017303903513184,75197869250518812754
%N A000699 Number of irreducible diagrams with 2n nodes.
%C A000699 Perturbation expansion in quantum field theory: spinor case in 4 spacetime 
               dimensions.
%D A000699 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000699 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000699 D. J. Broadhurst and D. Kreimer, Combinatoric explosion of renormalization 
               tamed by Hopf algebra: 30-loop Pad-Borel resummation. Phys. Lett. 
               B 475 (2000), 63-70.
%D A000699 M. Klazar, Non-P-recursiveness of numbers of matchings or linear chord 
               diagrams with many crossings, Advances in Appl. Math., Vol. 30 (2003), 
               pp. 126-136.
%D A000699 M. Klazar, Counting even and odd partitions, Amer. Math. Monthly, 110 
               (No. 6, 2003), 527-532.
%D A000699 Nijenhuis, Albert and Wilf, Herbert S., The enumeration of connected 
               graphs and linked diagrams, J. Combin. Theory Ser. A 27 (1979), no. 
               3, 356-359.
%D A000699 R. R. Stein, On a class of linked diagrams, I. Enumeration, J. Combin. 
               Theory, A 24 (1978), 357-366.
%D A000699 R. R. Stein and C. J. Everett, On a class of linked diagrams, II. Asymptotics, 
               Discrete Math., 21 (1978), 309-318.
%D A000699 J. Touchard, Sur un proble`me de configurations et sur les fractions 
               continues, Canad. J. Math., 4 (1952), 2-25.
%H A000699 T. D. Noe, <a href="b000699.txt">Table of n, a(n) for n=1..100</a>
%H A000699 D. J. Broadhurst and D. Kreimer, <a href="http://arXiv.org/abs/hep-th/
               9912093">Combinatoric explosion of renormalization ...</a>
%H A000699 P. Flajolet and M. Noy, <a href="http://algo.inria.fr/flajolet/Publications/
               FlNo00.pdf">Analytic Combinatorics of Chord Diagrams</a>
%F A000699 a(n) = (n-1)*Sum_{i=1..n-1} a(i)*a(n-i).
%e A000699 a(31)=627625976637472254550352492162870816129760 was computed using Kreimer's 
               Hopf algebra of rooted trees. It subsumes 2.6*10^21 terms in quantum 
               field theory.
%Y A000699 Cf. A004300, A051862.
%Y A000699 Sequence in context: A161120 A121063 A051863 this_sequence A138423 A158836 
               A086783
%Y A000699 Adjacent sequences: A000696 A000697 A000698 this_sequence A000700 A000701 
               A000702
%K A000699 nonn,easy,nice
%O A000699 1,3
%A A000699 N. J. A. Sloane (njas(AT)research.att.com).
%E A000699 More terms from David Broadhurst (D.Broadhurst(AT)open.ac.uk), Dec 14 
               1999