π\pi (...) something!

Algebra Level 5

If π(n)\pi(n) denotes product of all binomial coefficients in (1+x)n\left(1+ x\right)^n, then the ratio of π(2002)\pi(2002) to π(2001)\pi(2001) can be expressed as

2002mn!,\dfrac{2002^{m}}{n!},

where mm and nn are positive integers. Fin the minimum value of m+nm+n.


Image Credit: Wikimedia Pascal Triangle by Dohduhdah
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