Consider the polynomial function and its first-order derivative . The sums of the coefficients of P and P', are and , respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: etc. The total sum of this sequence converge to .
For this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, . Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.
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