Add to ORKGA generalized central trinomial coefficient Tn(b, c) is the coefficient of xn in the expansion of (x2+bx+c)n with b, c ∈ Z. In this paper we investigate congruences and series for sums of terms related to central binomial coefficients and generalized central trinomial coefficients. The paper contains many conjectures on congruences related to representations of primes by certain binary quadratic forms, and 62 proposed new series for 1/pi motivated b
Abstract. Much is known about binomial coefficients where primes are con-cerned, but considerably le...
The coefficient of each term in combinatorial geometric series refers to a binomial coefficient. Thi...
We establish integral identities for sums involving binomial coefficients and Harmonic numbers. Usi...
AbstractWe present several congruences for sums of the type ∑k=1p−1mkk−r(2kk)−1, modulo a power of a...
We consider a set of combinatorial sums involving the reciprocals of the central binomial coefficien...
In the paper, the authors collect several integral representations of the Catalan numbers and centra...
We present several polynomial congruences about sums with central binomial coefficients and harmonic...
We prove congruences, modulo a power of a prime p, for certain finite sums involving central binomia...
In this paper we establish some new congruences involving central binomial coefficients as well as C...
This paper presents a multinomial theorem on the binomial coefficients for combinatorial geometric s...
This paper presents a multinomial theorem on the binomial coefficients for combinatorial geometric s...
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
This paper presents binomial theorems on combinatorial identities that are derived from the binomial...
AbstractThe coefficients aτϱ, sometimes called “generalized binomial coefficients” in the expansion ...
This paper presents a summation of series of binomial coefficients in combinatorial geometric series...
Abstract. Much is known about binomial coefficients where primes are con-cerned, but considerably le...
The coefficient of each term in combinatorial geometric series refers to a binomial coefficient. Thi...
We establish integral identities for sums involving binomial coefficients and Harmonic numbers. Usi...
AbstractWe present several congruences for sums of the type ∑k=1p−1mkk−r(2kk)−1, modulo a power of a...
We consider a set of combinatorial sums involving the reciprocals of the central binomial coefficien...
In the paper, the authors collect several integral representations of the Catalan numbers and centra...
We present several polynomial congruences about sums with central binomial coefficients and harmonic...
We prove congruences, modulo a power of a prime p, for certain finite sums involving central binomia...
In this paper we establish some new congruences involving central binomial coefficients as well as C...
This paper presents a multinomial theorem on the binomial coefficients for combinatorial geometric s...
This paper presents a multinomial theorem on the binomial coefficients for combinatorial geometric s...
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
This paper presents binomial theorems on combinatorial identities that are derived from the binomial...
AbstractThe coefficients aτϱ, sometimes called “generalized binomial coefficients” in the expansion ...
This paper presents a summation of series of binomial coefficients in combinatorial geometric series...
Abstract. Much is known about binomial coefficients where primes are con-cerned, but considerably le...
The coefficient of each term in combinatorial geometric series refers to a binomial coefficient. Thi...
We establish integral identities for sums involving binomial coefficients and Harmonic numbers. Usi...