## r-simplex numbers

I've come across a situation in my research where I need to do quite a bit of arithmetic with r-simplex numbers (just to be clear these are of the form $T_r(k) = \frac{k(k+1) \ldots (k+r-1)} {r!}$) So I don't have to waste space proving the arithmetic rules, does anyone know a good reference?

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Those are binomial coefficients $k+r-1 \choose r$. It might help to know what types of identities you want to use. Also, what is the connection to algebraic topology? – Douglas Zare Jan 30 2011 at 11:23
A good reference: en.wikipedia.org/wiki/Pascal%27s_triangle – JBL Jan 30 2011 at 14:09