Calculate this sum

**dhiab** · August 28th 2009, 07:14 AM

Calculate :
$S = \sum\limits_{p = 0}^n {C_p^n p^2 } \left( { - 3} \right)^p <br />$

**Opalg** · August 28th 2009, 11:50 PM

Start with the binomial expansion $(1+x)^n = \sum_{p=0}^n{n\choose p}x^p$ . Differentiate, multiply by x, differentiate again, multiply by x again, then put x=–3.

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