Mersenne Lucas numbers and complete homogeneous symmetric functions

In this paper, we first introduce new definition of Mersenne Lucas numbers sequence as, for \(n≥ 2,\) \(mₙ=3mₙ₋₁-2mₙ₋₂\) with the initial conditions \(m₀=2\) and \(m₁=3\). Considering this sequence, we give Binet's formula, generating function and symmetric function of Mersenne Lucas numbers. By using the Binet's formula we obtain some well-known identities such as Catalan's identity, Cassini's identity and d'Ocagne's identity. After that, we give some new generating functions for products of \(% ( p,q) \)-numbers with Mersenne Lucas numbers at positive and negative indice.