We study a new kind of symmetric polynomials Pn(x1, . . . , xm) of degree n in m real variables, which have arisen in the theory of numerical semigroups. We establish their basic properties and find their representation through the power sums Ek =Pm j=1 x k j . We observe a visual similarity between normalized polynomials Pn(x1, . . . , xm)/χm, where χm = Qm j=1 xj , and a polynomial part of a partition function W (s, {d1, . . . , dm}), which gives the number of partitions of s ≥ 0 into m positive integers dj , and we put forward a conjecture about their relationship.