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.
Bala, comment in OEIS sequence A001008 (the conjecture proved here), March 4
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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.