the value of `overset(n)underset(r=2)(Simga)(-2)^(r ) |{:( .^(n-2)C_(r-2),,.^(n-2)C_(r-1),,.^(n-2)C_(r)),(-3,,1 ,,1),(2,,-1,,0):}| (n gt 2)`

the value of Sigma_(r=2)^(n) (-2)^(r ) |{:( ""^(n-2)C_(r-2),,""^(n-2)C_(r-1),,""^(n-2)C_(r)),(-3,,1 ,,1),(2,,-1,,0):}| (n gt 2)

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=

""^(n)C_(r+1)+^(n)C_(r-1)+2.""^(n)C_(r)=

""^(n-2)C_(r)+2""^(n-2)C_(r-1)+""^(n-2)C_(r-2) equals :

""^(n) C_(r+1)+2""^(n)C_(r) +""^(n)C_(r-1)=

""^(n)C_(r)+2""^(n)C_(r-1)+^(n)C_(r-2) is equal to

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

For ""^(n) C_(r) + 2 ""^(n) C_(r-1) + ""^(n) C_(r-2) =

the value of the determinant |{:(.^(n)C_(r-1),,.^(n)C_(r),,(r+1)^(n+2)C_(r+1)),(.^(n)C_(r),,.^(n)C_(r+1),,(r+2)^(n+2)C_(r+2)),(.^(n)C_(r+1),,.^(n)C_(r+2),,(r+3)^(n+2)C_(r+3)):}| is

Find the sum sum_(r=1)^(n) r^(2) (""^(n)C_(r))/(""^(n)C_(r-1)) .