#1432 · Algebra · Linear equations

Sum of squared binomial coefficients

If $c_0, c_1, c_2,
ot_dots, c_n $d e n o t e t h ecoe f f i c i e n t s in t h ee x p an s i o n o f$ (1+x)^n $, p r o v e t ha t$ c_0^2 + c_1^2 + c_2^2 + \dots + c_n^2 = \frac{(2n)!}{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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