We consider the (direct sum over all n ∈ ℕ of the) K-theory of the semi-nilpotent commuting variety of gln, and describe its convolution algebra structure in two ways: the first as an explicit shuffle algebra (i.e., a particular ℤ[q1±1, q2±1]-submodule of the equivariant K-theory of a point) and the second as the ℤ[q1±1, q2±1]-algebra generated by certain elements {H̄n,d}(n,d)∈ℕ×ℤ. As the shuffle algebra over ℚ(q1, q2) has long been known to be isomorphic to half of an algebra known as quantum toroidal gl1, we thus obtain a description of an important integral form of the quantum toroidal algebra.