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{\bf Part II of  Computing Determinants Involving Stirling Numbers }
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{\it Tewodros AMDEBERHAN and Shalosh B. EKHAD }


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Using the Jacobi-Trudi formula mentioned in Theorem 2 in Part I (Eq. (I.3.5) in [M], p.4.1) we computed explicit expressions for
$\beta_n(a,b)$, as well as the explicit generating functions $\sum_{n=0}^{\infty} \beta_n(a,b) q^n$ (that are always rational functions of $q$).
for {\bf all} $10 \geq n \geq a \geq b \geq 0$.


The output file is

{\tt https://sites.math.rutgers.edu/\~{}zeilberg/tokhniot/oStirlingDet1.txt}  \quad.

It was generated by executing the command

{\tt Paper1(10,n,q):}

in the Maple package accompanying this article, that can be gotten from.

{\tt https://sites.math.rutgers.edu/\~{}zeilberg/tokhniot/StirlingDet.txt} \quad.

{\bf References}

[M] Ian G. Macdonald, {\it ``Symmetric Functions and Hall Polynomials''}, second edition, Clarendon Press, Oxford, 1995.

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Shalosh B. Ekhad, c/o D. Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen
Rd., Piscataway, NJ 08854-8019, USA. \hfill\break
Email: {\tt ShaloshBEkhad at gmail dot com}   \quad .
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Doron Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen
Rd., Piscataway, NJ 08854-8019, USA. \hfill\break
Email: {\tt DoronZeil at gmail  dot com}   \quad .


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