This has been uploaded to arXiv and submitted to Online Journal of Combinatorics. Interestingly, it was rejected by Electronic Journal of Combinatorics without refereeing, as being out of scope. It improves on previous work mainly by giving explicit formulae. The main work associated with this paper is the SAGE implementation by Alex Raichev. Computation of higher order asymptotic expansions by hand is essentially impossible, hence the paucity of numerical or explicit results in published papers.