  Take a multiplicative monoid of sequences in which the multiplication is
given by Hadamard product. The set of linear combinations of interleaving
monoid elements then yields a ring. We consider such a construction for the
monoid of hypergeometric sequences, yielding what we call the ring of
hypergeometric-type sequences -- a subring of the ring of holonomic sequences.
We present two algorithms in this setting: one for computing holonomic
recurrence equations from hypergeometric-type normal forms and the other for
finding products of hypergeometric-type terms. These are newly implemented
commands in our Maple package $\texttt{HyperTypeSeq}$, which we also describe.
