Sum over k of n Choose k by x to the k by kth Harmonic Number

Theorem

 * $\displaystyle \sum_{k \mathop = 1}^n \binom n k x^k H_k = \left({x + 1}\right)^n \left({H_n - \ln \left({1 + \frac 1 x}\right)}\right)$

where:
 * $\dbinom n k$ denotes a binomial coefficient
 * $H_k$ denotes the $k$th harmonic number.