A352175 The number of Feynman graphs in phi^3 theory with 2n vertices, 2 external legs.

1, 5, 30, 186, 1276, 9828, 86279, 866474, 9924846, 128592118, 1864888539, 29950693288, 527584198445, 10109318656565, 209256249845854, 4651751087878667, 110501782280985273, 2792991694461152344, 74832356485576239136, 2118333127408342718683, 63169771935593153194107

Offset: 0

Author

R. J. Mathar, Mar 07 2022

Keywords

• nonn

Comments

a(n) is the number of multigraphs with 2n unlabeled nodes of degree 3 plus 2 noninterchangeable nodes of degree 1, loops allowed. - Andrew Howroyd, Mar 10 2023

Links

• R. de Mello Koch and S. Ramgoolam, Strings from Feynman graph counting: Without large N, Phys. Rev. D 85 (2012) 026007, App. D.
• R. J. Mathar, Illustrations

Crossrefs

Cf. A129427 (no external legs), A352173 (degree 4 case), A361447 (connected).

Extensions

a(0) prepended and terms a(9) and beyond from Andrew Howroyd, Mar 10 2023