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笔者发现并证明一个神奇有用的组合数不等式,进而推出一系列十分有趣的组合数恒等式.公式:Cnm++kkCkm++rkCkr+r=Cnn+kCnmCrm(1)证左端=(n+k)!(m+k)!(n-m)!·(m+k)!(k+1)!(m-r)!·(k+r)!r!k!=(n+k)!k!n!·n!m!(n-m)!·m!r!(m-r)!=右端.从而(1)式获证.由(1)式可推出一系列组合数?
The author found and proved a magical useful combination number inequality, and then introduced a series of very interesting combination number identities. Formula: Cnm++kkCkm++rkCkr+r=Cnn+kCnmCrm(1) left=(n+k)! (m+k)!(nm)!(m+k)!(k+1)!(mr)!(k+r)!r!k!=(n+k)!k!n!· n!m!(nm)!m!r!(mr)!=Right end. Thus (1) is certified. A series of combinations can be derived from (1).