Summations Involving Binomial Coefficients

Author: Katsuura, Hidefumi

Source: The College Mathematics Journal, Volume 40, Number 4, September 2009 , pp. 275-278(4)

Publisher: Mathematical Association of America

Buy & download fulltext article:

OR

Price: $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?
Related content

Tools

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

Text size:

A | A | A | A
Share this item with others: These icons link to social bookmarking sites where readers can share and discover new web pages. print icon Print this page