Find the sum `sumsum_(i!=j)^ nC_i^n C_j`

Find the sum sumsum_(0lt=ilt=jlt=n)^ nC_i^n C_j

Find the sum sumsum_(0leiltjlen)"^nC_i

Find the sum sumsum_(0leiltjlen) "^nC_i "^nC_j

Find the sum sum_(j=0)^(n) (""^(4n+1)C_(j)+""^(4n+1)C_(2n-j)) .

Find the sum sum_(i=0)^r.^(n_1)C_(r-i) .^(n_2)C_i .

Find the sum sum_(j=1)^(10)sum_(i=1)^(10)ixx2^(j)

Find the value of sumsum_(0lt=i

If (1+x)^n=C_0+C_1x+C_2x^2+.......+C_n x^n , then show that the sum of the products of the coefficients taken two at a time, represented by sumsum_(0lt=iltjlt=n) "^nc_i "^n c_j is equal to 2^(2n-1)-((2n)!)/ (2(n !)^2)

The sum sumsum_(0leilejle10) (""^(10)C_(j))(""^(j)C_(r-1)) is equal to

Find the sum Sigma_(j=1)^(n) Sigma_(i=1)^(n) I xx 3^j