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Results tagged with binomial-coefficients
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user 4794
For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.
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How to prove this polynomial always has integer values at all integers?
$$P_m(x)=\sum_{i=0}^{m}\sum_{j=0}^{m}\binom{x+j}{ j}\binom{x-1}{ j}\binom{j}{ i}\binom{m}{ i}\binom{i}{ m-j}\frac{3}{(2i-1)(2j+1)(2m-2i-1)}.$$
Our task is to show it takes integer values on integers. …
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