This page is an appendix to the paper Asymptotic enumeration of symmetric integer matrices with uniform row sum, by Brendan D. McKay and Jeanette C. McLeod, arXiv:1108.4496v1.
Define M(n,k) to be the number of loop-free multigraphs which have n vertices and are regular of degree k.
Equivalently, M(n,k) is the number of n-by-n symmetric nonnegative integer matrices with zero diagonal and all row sums equal to k.
The Maple file symmint.maple defines a function M(n,k) which can compute M(n,k) for these values:
symmint.maple can be used in a Maple session (console or worksheet) by inputting it with the "read" command. It is a plain text file, so if you only want the numbers without running Maple you can just look at it.
Page Master: Brendan McKay, bdm@cs.anu.edu.au and http://cs.anu.edu.au/~bdm.