This paper presents a simple approach to invert the matrix P n + I n by applying the Euler polynomials and Bernoulli numbers, where P n is the Pascal matrix.

In this paper, the author gives a simpler alternative approach to the LU factorization and 1-banded factorization of the Vandermondematrix, and obtains explicit formulas of the triangular factors andâ€¦ (More)

By a Taylor expansion of a generating function, we mean that the remainder of the expansion is a functional of the generating function itself. In this paper, we consider the Taylor expansion for theâ€¦ (More)

Let n be a positive integer. For each integer k â‰¥ 0, let Z(n, k) denote the sum of k-th powers of positive integers, i.e., Z(n, k) = 1 + 2 + Â· Â· Â· + n, which is usually called the sum of integerâ€¦ (More)

By presenting Riordan matrix as a triangle, the central coefficients are entries in the central column. Starting at the central column, the r-shifted central coefficients are entries in column r ofâ€¦ (More)