  By applying p-adic integral on the set of p-adic integers in [27]
(Interpolation Functions for New Classes Special Numbers and Polynomials via
Applications of p-adic Integrals and Derivative Operator, Montes Taurus J. Pure
Appl. Math. 3 (1), ...--..., 2021 Article ID: MTJPAM-D-20-00000), we
constructed generating function for the special numbers and polynomials
involving the following combinatorial sum and numbers:
  y(n,\lambda )=\sum_{j=0}^{n}\frac{(-1)^{n}}{(j+1)\lambda ^{j+1}\left(\lambda
-1\right) ^{n+1-j}}
  The aim of this paper is to use the numbers y(n,{\lambda}) to derive some new
and novel identities and formulas associated with the Bernstein basis
functions, the Fibonacci numbers, the Harmonic numbers, the alternating
Harmonic numbers, binomial coefficients and new integral formulas for the
Riemann integral. We also investigate and study on open problems involving the
numbers y(n,{\lambda}) in [27]. Moreover, we give relation among the numbers
y(n,(1/2)), the Digamma function, and the Euler constant. Finally, we give
conclusions for the results of this paper with some comments and observations.

Combinatorics