On a partition theorem of MacMahon-Andrews

Recently, George Andrews [1] proved the following partition theorem, generalizing an earlier result of MacMahon [2, p. 54] (which deals with the case r = 1): The number of partitions of n, in which a part occurring an odd number of times occurs at least (2r+1) times, equals the number of partitions of n into parts which are either even or else = 2r+1 (mod 4r+2). We wish to remark that Andrews' theorem is itself a special case of the following result.