OFFSET

0,2

COMMENTS

The generating function of this is the product of the g.f. of the connected diagrams (A352174) by the g.f. of the vacuum diagrams (A129429, including a term x^0 for the empty graph): x + 2*x^2 + 7*x^3 + 23*x^4 + ... = (x + x^2 + 3*x^3 + 10*x^4 + ...) * (1 + x + 3*x^2 + 7*x^3 + 20*x^4 + ...). - R. J. Mathar, Mar 05 2023

a(n) is the number of multigraphs with n unlabeled nodes of degree 4 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.

CROSSREFS

KEYWORD

nonn

AUTHOR

R. J. Mathar, Mar 07 2022

EXTENSIONS

Offset corrected and a(13) and beyond from Andrew Howroyd, Mar 10 2023

STATUS

approved