[seqfan] conjectures on hypergeometric recurrences for central k-nomial numbers

Richard Mathar mathar at strw.leidenuniv.nl
Tue Feb 23 14:34:04 CET 2010

In work related to http://arxiv.org/abs/1002.3844 I've basically
formulated conjectures in hypergeometric recurrence format for the
3-nomial, 5-nomial and 7-nomial central coefficients without any
formal verification (a.k.a. "proof"). These are in A097861, A005191 and A025012.
Given that there seem to be "closed" forms of these terms as sums
over products of binomials, I'd encourage everyone with a good sense of the
WZ methods (or ability to handel them via the associated differential equations)
to bite at these. They are tested along the first 300 terms of each
sequence and are likely correct.

Richard Mathar

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