(Cn0)2+(Cn1)2+(Cn2)2+...+(Cnn)2=(C2nn)2(C^{0}_{n})^{2} + (C^{1}_{n})^{2} + (C^{2}_{n})^{2} + ...+ (C^{n}_{n})^{2} = (C^{n}_{2n})^{2}

Cn1+2Cn2+3Cn3+...+nCnn=n2n1C^{1}_{n} + 2C^{2}_{n} + 3C^{3}_{n} +...+nC^{n}_{n} = n2^{n-1}

Cn1+22Cn2+32Cn3+...+n2Cnn=n(n+1)2n1C^{1}_{n} + 2^{2}C^{2}_{n} + 3^{2}C^{3}_{n} +...+n^{2}C^{n}_{n} = n(n+1)2^{n-1}