N=4 supersymmetric linear W∞ [λ] algebra

From the recently known N=2 supersymmetric linear W∞K,K[λ] algebra where K is the dimension of the fundamental (or antifundamental) representation of the bifundamental βγ and bc ghost system, we determine its N=4 supersymmetric enhancement at K=2. We construct the N=4 stress energy tensor, the first N=4 multiplet, and their operator product expansions (OPEs) in terms of the above bifundamentals. We show that the OPEs between the first N=4 multiplet and itself are the same as the corresponding ones in the N=4 coset SU(N+2)SU(N) model under the large (N,k) 't Hooft-like limit with fixed λco(N+1)(k+N+2), up to two central terms. The two parameters are related to each other, λ=12λco. We also provide other OPEs by considering the second, the third, and the fourth N=4 multiplets in the N=4 supersymmetric linear W∞[λ] algebra.