\[ \large \dbinom{n}{a} \ , \ \dbinom{n}{a+1} \, \ \ldots \ , \ \dbinom{n}{a+b} \]

For positive integers \(n,a,b\) with \(n > a+b \), the above sequence of numbers follow an arithmetic progression. Find the maximum value of \(b\).

**Clarification**: The numbers above are all written in binomial coefficient form.

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