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Quoting:

We define $f(d, n)$ to be the number of integers of up to $d$ decimal digits with digit sum less than or equal to $n$. It can be seen that this function is given by the formula $$f(d,n)=\sum_{i=0}^d(-1)^i\binom{d}i\binom{n+d-10i}d\;.$$

How is this derived? And surely the function requires binomials with negative arguments?

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    Please edit your question to make it self-contained, and please edit the title to make it more informative.2012-04-25
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    Edited to reflect this2012-04-25

1 Answers 1