In the study of Zeilberger's conjecture on an integer sequence related to the Catalan numbers, Lassalle proposed the following conjecture. Let (t) n denote the rising factorial, and let Λ R denote the algebra of symmetric functions with real coefficients. If ϕ is the homomorphism from Λ R to R defined by ϕ(h n ) = 1/((t) n n!) for some t > 0, then for any Schur function s λ , the value ϕ(s λ ) is positive. In this paper, we provide an affirmative answer to Lassalle's conjecture by using the Laguerre-Pólya-Schur theory of multiplier sequences.