Conjecture of Andrews on Partitions

Definition 1.2. For an even integer λ, let Aλ,k,a(n) denote the number of partitions of n into parts such that no part which is not equivalent to 0(mod λ+ 1) may be repeated and no part is equivalent to 0,±(a−λ/2)(λ+1)mod[(2k−λ+1)(λ+1)]. For an odd integer λ, let Aλ,k,a(n) denote the number of partitions of n into parts such that no part which is not equivalent to 0(mod((λ+1)/2)) may be repeated, no part is equivalent to λ+1(mod2λ+2), and no part is equivalent to 0,±(2a−λ)((λ+ 1)/2)mod[(2k−λ+1)(λ+1)].