20 citations · 29 across the 11 of their papers we have counts for
12 papers
A Family of Generating Functions for Reciprocal Binomial Coefficients and Its Applications
Dmitry Kruchinin, Vladimir Kruchinin
A generating function for reciprocal binomial coefficients is written down, integral representations of this function are obtained, generating functions for sums of reciprocal bino…
Algorithms for ranking and unranking the combinatorial set of RNA secondary structures
Yuriy Shablya, Dmitry Kruchinin
In this paper, we study the combinatorial set of RNA secondary structures of length with base-pairs. For a compact representation, we encode an RNA secondary structure by t…
A generating function for the Euler numbers of the second kind and its application
Dmitry V. Kruchinin, Vladimir V. Kruchinin
In the paper, 2 explicit formulas for the Euler numbers of the second kind are obtained. Based on those formulas a exponential generating function is deduced. Using the generating…
Explicit formulas for enumeration of lattice paths: basketball and the kernel method
Cyril Banderier, Christian Krattenthaler, Alan Krinik +4
This article deals with the enumeration of directed lattice walks on the integers with any finite set of steps, starting at a given altitude and ending at a given altitude ,…
Method for solving an iterative functional equation
Dmitry Kruchinin, Vladimir Kruchinin
Using the notion of the composita, we obtain a method of solving iterative functional equations of the form , where , . We pro…
Integer properties of a composition of exponential generating functions
Dmitry Kruchinin
In this paper, we study a composition of exponential generating functions. We obtain new properties of this composition, which allow to distinguish prime numbers from composite num…
Application of a composition of generating functions for obtaining explicit formulas of polynomials
Vladimir Kruchinin, Dmitry Kruchinin
Using notions of composita and composition of generating functions we obtain explicit formulas for Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated L…
A Method for Obtaining Generating Function for Central Coefficients of Triangles
Vladimir Kruchinin, Dmitry Kruchinin
We present techniques for obtaining a generating function for the central coefficients of a triangle , which is given by the expression $[xH(x)]^k=\sum_{n\geqslant k} T(n,k…
The number of multinomial coefficients based on a set of partitions of n into k parts and divided by k evenly
Dmitry Kruchinin
In this paper we obtained an original integer sequence based on the properties of the multinomial coefficient. We investigated a property of the sequence that shows connection with…
On a property of superposition of the generating functions ln(1/(1-F(x)))
Dmitry Kruchinin
Obtained a new property of superposition of the generating functions ln(1/(1-F(x))), where F(x) - generating function with integer coefficients, which allows the construction a pri…
New properties for a composition of some generating functions for primes
Dmitry Kruchinin, Yuriy Shablya
In this paper, we consider properties of coefficients of a generating functions composition, where the outer function is a logarithmic generating function and the inner function is…
Composita and its properties
Vladimir V. Kruchinin, Dmitry V. Kruchinin
In this paper we study the coefficients of the powers of an ordinary generating function and their properties. A new class of functions based on compositions of an integer is i…