Skip to main content

Summations Involving Binomial Coefficients

Buy Article:

$20.00 plus tax (Refund Policy)

Abstract:

We prove following two conjectures of Thomas Dence:

Conjecture 1: Let n and k be odd positive integers with kn. Then

(n–1)/2j = 0(n; j)(–1)j(n – 2j)k = {0 if k < n; 2n–1 · n! if k = n.

Conjecture 2: Let n and k be even positive integers with kn. Then

(n–2)/2j = 0(n; j)(–1)j(n – 2j)k = {0 if k < n; 2n–1 · n! if k = n.

Document Type: Research Article

DOI: http://dx.doi.org/10.4169/193113409X458723

Publication date: September 1, 2009

More about this publication?
maa/cmj/2009/00000040/00000004/art00006
dcterms_title,dcterms_description,pub_keyword
6
5
20
40
5

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
X
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more