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Let f(n), g (n) be polynomial in n and l...

Let f(n), g (n) be polynomial in n and let
`Delta_(r)=|{:(r^(2).C_(r),n(n+1)2^(n-2),f(n)),(6r(n-r+1),n(n+1)(n+2),g(n)),(4(5^(r-1)),5^(n)-1,h(n)):}|`, then evaluate `underset(r=1)overset(n)sum Delta_(r)`.
(use `(1+x)^(n)=underset(r=0)overset(n)sum(C_(r)x^(r))`)

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