The nth harmonic number H_n equals (1/m) times the sum from k=1 to n of (-1)^{k+1}/k times binom(mk, k) times binom(n+(m-1)k, n-k), for every nonzero integer m.
"" 10 11from fractions import Fraction 12from math import comb 13 A GENERAL-mHARMONIC-NUMBER IDENTITY 7 14 15def harmonic(n: int) -> Fraction: 16
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A Proof of Bala's General-$m$ Representation of the Harmonic Numbers
The nth harmonic number H_n equals (1/m) times the sum from k=1 to n of (-1)^{k+1}/k times binom(mk, k) times binom(n+(m-1)k, n-k), for every nonzero integer m.