chapter
Remark 15.17.
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Remark 15.17. If x ∈ N0, x ≤ n, the second term vanishes, so the right side becomes just

(−1)n(n− 1)!,

independent of x. The case x = n is found in [Kaucky´ 75, (6.7.2)].

A similar but more specialized formula is the following:

Theorem 15.18. For all p ∈ N, n∑

( n

k

) [−p]k[p]n−kHp+k−1 = (−1)n(n− 1)!. (15.12)

Proof: We write the sum as

[p]nHp−1 + n∑

( n

k

) [−p]k[p]n−kHp+k−1.