# It does not exist

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

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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