  In this paper, we discuss a method that utilizes the recurrence of $A_{n,k}$
to solve summations of the form $\sum_{k=n_0}^{n} A_{n,k}$. It is observed that
by repeating the procedure, the upper bound of summation is reduced and tilts
toward the lower bound. This method of summation is mostly suitable for
combinatorial sequences such as binomial coefficients, Stirling numbers of both
kinds, etc. After the main method is displayed, some examples are illustrated.
Some useful identities about Stirling and r-Stirling numbers are obtained.
Finally, two transforms called rising and falling factorial transforms which
turn the basis of power polynomials into factorial basis are derived. These
transforms verify and simplify the results obtained in the examples section.
Also, these transforms describe the relationship between fractional derivatives
(or fractional integrals) and falling factorial (or rising factorial) by its
series expansion.
