All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

We construct all solvable Lie algebras with a specific n-dimensional nilradical n(n,2) (of degree of nilpotency n - 1 and with an (n - 2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.