1,3

Perturbation expansion in quantum field theory: spinor case in 4 spacetime dimensions.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

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.

M. Klazar, Counting even and odd partitions, Amer. Math. Monthly, 110 (No. 6, 2003), 527-532.

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.

R. R. Stein, On a class of linked diagrams, I. Enumeration, J. Combin. Theory, A 24 (1978), 357-366.

R. R. Stein and C. J. Everett, On a class of linked diagrams, II. Asymptotics, Discrete Math., 21 (1978), 309-318.

J. Touchard, Sur un proble`me de configurations et sur les fractions continues, Canad. J. Math., 4 (1952), 2-25.

T. D. Noe, Table of n, a(n) for n=1..100

D. J. Broadhurst and D. Kreimer, Combinatoric explosion of renormalization ...

P. Flajolet and M. Noy, Analytic Combinatorics of Chord Diagrams

a(n) = (n-1)*Sum_{i=1..n-1} a(i)*a(n-i).

a(31)=627625976637472254550352492162870816129760 was computed using Kreimer's Hopf algebra of rooted trees. It subsumes 2.6*10^21 terms in quantum field theory.

Cf. A004300, A051862.

Sequence in context: A161120 A121063 A051863 this_sequence A138423 A158836 A086783

Adjacent sequences: A000696 A000697 A000698 this_sequence A000700 A000701 A000702

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from David Broadhurst (D.Broadhurst(AT)open.ac.uk), Dec 14 1999