In this paper, we will investigate and evaluate, in closed forms, three binomial sums weighted by falling and rising factorials. We first use the relationships between the rising, falling factorials and the binomial coefficients. Then we rewrite the claimed identities in terms of generalized hypergeometric functions to prove the claimed results.
"Three binomial sums weighted by falling and rising factorials,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/11