#1432 · Algebra · Linear equations

Sum of squared binomial coefficients

If $c_{0}, c_{1}, c_{2}, \dots, c_{n}$ denote the coefficients in the expansion of $(1 + x)^{n}$ , prove that $c_{0}^{2} + c_{1}^{2} + c_{2}^{2} + \dots + c_{n}^{2} = \frac{( 2 n )!}{n ! n !}$ .

~10 minProof · checked by AIBinomial TheoremVandermonde's Identity

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIII. Binomial Theorem: Positive Integral Index, Examples XIII.b, No. 22

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