Counting Distinct Diagrams in Scalar Field Theory

[whynothis]

I was just trying to think of a simple relation to find the number of distinct diagrams to a given order within a theory (specifically I am thinking of a $$\phi^{4}$$ scalar theory). I am reading Tony Zee's book and am working through his "baby problem" where he expands the integral:

$$\int_{-\inf}^{\inf} dq e^{-\frac{1}{2}m^{2}q^{2}+Jq-\frac{\lambda}{4!}q^{4}$$

in both in powers of $$\lambda$$ and J so that we can pick out diagrams to a specific order in both.

So is there a way to find the total number of distinct diagrams to order $$(\lambda^{n},J^{m})$$?

Thanks in Advanced

 

[zeion]

to be honest, i have no idea.

 

[K^2]

From personal experience, you just keep working these out by hand until you see a pattern. Or you get to a point where you give up. If there is a better way, I have not found it.