Improved bounds for and the factorical polynomial.
Improved bounds on the number of ways of expressing as a binomial coefficient.
Integer sequences and matrices over finite fields.
Integral representations and binomial coefficients.
Integral representations of Catalan and related numbers.
Integrals and polygamma representations for binomial sums.
Integrals of logarithmic and hypergeometric functions
Integrals of logarithmic and hypergeometric functions are intrinsically connected with Euler sums. In this paper we explore many relations and explicitly derive closed form representations of integrals of logarithmic, hypergeometric functions and the Lerch phi transcendent in terms of zeta functions and sums of alternating harmonic numbers.
Inverse series relations, formal power series and Blodgett-Gessel's type binomial identities.
Inversions of permutations in symmetric, alternating, and dihedral groups.