For n ≥ 3 and s ≤ 92, it is proved in [4] that, except for finitely many pairs (n, s), G 1 (x) = G 1 (x, n, s) is either irreducible or linear factor times an irreducible polynomial. If s ≤ 30, we determine here explicitely the set of pairs (n, s) in the above assertion. This implies a new proof of the result of Nair and Shorey [3] that G 1 (x) is irreducible for s ≤ 22.
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