What is the coefficient of $x^{n-1}$ in $$(x+1)^{n}+(x+1)^{n+2}+(x+1)^{n+4}+\dots+(x+1)^{n+2m}\;,$$ where $x,n,m$ are positive integers? Is there a closed form answer?
Help needed on a problem regarding diffcult manipulation of binomial coefficients
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binomial-coefficients
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0I was just wondering if there are relationship between the coefficient of $x^{n-1}$ in $(x+1)^n+(x + 1)^{n+2}+... +(x+1)^{n+2m}$ and the coefficient of $x^{n-1}$ in $(x+1)^{n-1}+(x+1)^{n+1}+... +(x+1)^{n+2m-1}$. – 2012-02-21