Geodesic
A New Identity and Some Applications
Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 281-290

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DOI

Let (n|k) denote the number of k-choices 1≤x1<x2<...<xk≤n satisfying xi-xi-1≥2, i = 2,..., k, n + x1-xk≥2; let (m, n | k) = Σi+j=k (m | i)(n | j). Several elementary proofs of the new identity (m, n|k) = (m + n | k) if 0≤k<m≤n. and if 0≤m≤n, m≤k, are given. Generalizations and applications are considered. 
Moser, W. O. J.; Pollack, Richard. A New Identity and Some Applications. Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 281-290. doi: 10.4153/CMB-1980-039-0
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