To prove the formula just before Section 378 on p. 364 in Lectures in Quaternions, I need:
(1) for 1<=k<=n-m, the number of associative decompositions of k + m pairwise noncommuting factors into products of m+1 expressions is (1/m!)k(k+1)...(k+m-1); (2) Sum(from k = 1 to k = n-m) of [(1/m!)k(k+1)...(k+m-1)][(n+1)-(k+m)] =[(n+1)n...(n-m)]/(m+2)!
If anyone has a correction or reference in a website/text/handbook (e.g. Henry Gould's Combinatorial Identities), I would much appreciate it.