[seqfan] Need help with seqs from 2-D g.f.'s

[Neil Sloane]

Dear Seq Fans, Given a generating function of 2 variables, f(x,y),
the diagonal sequence it produces is a(n) = coefft of x^n*y^n.

This paper:
Robin Pemantle and Mark C. Wilson, Twenty Combinatorial Examples of
Asymptotics Derived from Multivariate Generating Functions, SIAM Rev., 50
(2008), 199-.
studies a bunch of these. There is a list on page 201. They don't
give the actual numbers, and they certainly don't mention the OEIS.

A recent arXiv paper
Stephen Melczer and Bruno Salvy, Symbolic-Numeric Tools for Analytic
Combinatorics in Several Variables, arXiv:1605.00402, 2016.
gives more examples, again without numbers or OEIS references.

Could someone help by working out the initial terms, adding the sequences to
the OEIS if they are missing, and adding references to these papers?
I can send the Pemantle paper to anyone who wants to help.