  In this article, we introduce and study a new integer sequence referred to as
the higher order Mersenne sequence. The proposed sequence is analogous to the
higher order Fibonacci numbers and closely associated with the Mersenne
numbers. Here, we discuss various algebraic properties such as Binet's formula,
Catalan's identity, d'Ocagne's identity, generating functions, finite and
binomial sums, etc. of this new sequence, and some inter-relations with
Mersenne and Jacobsthal numbers. Moreover, we study the sequence generated from
the binomial transforms of the higher order Mersenne numbers and present the
recurrence relation and algebraic properties of them. Lastly, we give matrix
generators and tridiagonal matrix representation for higher order Mersenne
numbers.
