The paper proves Knuth's old sum in two lines and derives a v-parameter generalization with many corollary identities.
Prodinger, Knuth old sum - a survey, EACTS Bulletin 52 (1994), 232--245
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A Short Proof of Knuth's Old Sum
The paper proves Knuth's old sum in two lines and derives a v-parameter generalization with many corollary identities.