Harmonic Numbers and Cubed Binomial Coefficients

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Harmonic Numbers and Cubed Binomial Coefficients

Anthony Sofo Victoria University College, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, Australia Correspondence should be addressed to Anthony Sofo, [email protected] Received 18 January 2011; Accepted 3 April 2011 Academic Editor: Toufik Mansour Copyright q 2011 Anthony Sofo. This is an open access article distributed under the Creative Commons Attribution License, which...

متن کامل

Series with Central Binomial Coefficients, Catalan Numbers, and Harmonic Numbers

We present several generating functions for sequences involving the central binomial coefficients and the harmonic numbers. In particular, we obtain the generating functions for the sequences ( 2n n ) Hn, ( 2n n ) 1 nHn, ( 2n n ) 1 n+1Hn , and ( 2n n ) n m. The technique is based on a special Euler-type series transformation formula.

متن کامل

Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers

A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain fin...

متن کامل

Interesting Series Associated with Central Binomial Coefficients, Catalan Numbers and Harmonic Numbers

We establish various generating functions for sequences associated with central binomial coefficients, Catalan numbers and harmonic numbers. In terms of these generating functions, we obtain a large variety of interesting series. Our approach is based on manipulating the well-known generating function of the Catalan numbers.

متن کامل

Catalan Triangle Numbers and Binomial Coefficients

The binomial coefficients and Catalan triangle numbers appear as weight multiplicities of the finite-dimensional simple Lie algebras and affine Kac–Moody algebras. We prove that any binomial coefficient can be written as weighted sums along rows of the Catalan triangle. The coefficients in the sums form a triangular array, which we call the alternating Jacobsthal triangle. We study various subs...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: International Journal of Combinatorics

سال: 2011

ISSN: 1687-9163,1687-9171

DOI: 10.1155/2011/208260