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MultipleHarmonicNumber

The finite multiple harmonic sum over strictly decreasing indices n >= i1 > ... > ik >= 1 of Product[1/ij^sj].

$ wo 'MultipleHarmonicNumber[3, {2, 1}]'
5/12

A single weight reduces to the ordinary harmonic number.

$ wo 'MultipleHarmonicNumber[6, {1}]'
49/20