Abstract
It is shown that there are infinitely many formulas to calculate multiplicities of weights participating in irreducible representations of
A
N
Lie algebras. On contrary to recursive character of Kostant and Freudenthal multiplicity formulas, they provide us systems of linear algebraic equations with N-dependent polinomial coefficients. These polinomial coefficients are in fact related with polinomials which represent eigenvalues of Casimir operators.