A Study on Hyperbolic Generalized Guglielmo Numbers

In this paper, we introduce the generalized hyperbolic Guglielmo numbers. We delve into various specific instances, including hyperbolic triangular numbers, hyperbolic triangular-Lucas numbers, hyperbolic oblong numbers, and hyperbolic pentagonal numbers. We present Binet’s formulas, generating functions and summation formulas for these numbers. Furthermore, Catalan’s and Cassini’s identities and matrices associated with these sequences will be provided deeply.