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Binomial expansion generates the Pascal triangle but what does it generate when you have different amount of terms there?

You can see here the geometric generation with only 2 terms. I am interested to know if you have many terms.

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Do you mean Pascal's triangle? What is up with z and h? How many terms are inside parentheses? Do you mean something like $(a_1+a_2+\cdots+a_k)^n$ where $k$ is an integer greater than $2$? You get multinomial coefficients: Is that what you're looking for? – Jonas Meyer Jul 9 '11 at 0:20
@Jonas Meyer: yes, thanks. – hhh Jul 9 '11 at 1:07
@hhh: feel free to edit the question! – The Chaz 2.0 Jul 9 '11 at 4:21
up vote 5 down vote accepted

See: multinomial theorem

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In particular, see the section Generalized Pascal's triangle and the articles linked there, Pascal's pyramid and Pascal's simplex – Jonas Meyer Jul 9 '11 at 0:30

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