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ERIC Number: EJ1013330
Record Type: Journal
Publication Date: 2013
Pages: 12
Abstractor: As Provided
Reference Count: 5
ISSN: ISSN-0020-739X
A Note on a Family of Alternating Sums of Products of Binomial Numbers
Gauthier, N.
International Journal of Mathematical Education in Science and Technology, v44 n2 p253-264 2013
We study the following family of integral-valued alternating sums, where -infinity equal to or less than m equal to or less than infinity and n equal to or greater than 0 are integers [equation omitted]. We first consider h[subscript m](n) for m and n non-negative integers and show that it is of the form 2[superscript n + 2m] - P[subscript m](n), where P[subscript m]n may be represented as a polynomial of degree m in n, or expressed as a non-polynomial closed form given by a sum of binomial numbers. We then consider h[subscript m]n for m = -ImI a negative integer and for n a non-negative integer. This reveals, in particular, that h[subscript-ImI]n = 0 for 0 equal to or less than n equal to or less than ImI, that h[subscript-ImI](n) = 2[superscript n-2ImI] for n equal to or greater than 2ImI. We also show that h[subscript-ImI](n + ImI) is a polynomial of degree n - 1 in ImI, for fixed n equal to or greater than I, with ImI equal to or greater than I, and we give expressions for the coefficients.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A