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Jonah Formula

A formula for the generalized Catalan Number ${}_pd_{qi}$. The general formula is

{n-q\choose k-1}=\sum_{i=1}^k {}_pd_{qi}{n-pi\choose k-i},

where ${n\choose k}$ is a Binomial Coefficient, although Jonah's original formula corresponded to $p=2$, $q=0$ (Hilton and Pederson 1991).


Hilton, P. and Pederson, J. ``Catalan Numbers, Their Generalization, and Their Uses.'' Math. Intel. 13, 64-75, 1991.

© 1996-9 Eric W. Weisstein