What is the coefficient of $z^k$ in ${z+n-1 \choose n}$ for $1 \leq k \leq n$? Thanks. I'm currently looking into Stirling numbers of the first kind, as it seems there is a connection.
What is the coefficient of $z^k$ in ${z+n-1 \choose n}$ for $1 \leq k \leq n$?
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combinatorics
binomial-coefficients
stirling-numbers
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1We prefer questions not to be entirely contained in titles. – 2012-10-02