We investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Applying the proposed identities to power sequences and the sequence of Pochhammer numbers, we recover and generalize known recursive relations. Restricting to the cosine of fractional angles, we then study the special case of the family of k-generalized Fibonacci numbers, and present general recursions and identities which link these sequences.