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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The number of binomial coefficients divisible by a fixed power of $ 2$


Author: F. T. Howard
Journal: Proc. Amer. Math. Soc. 29 (1971), 236-242
MSC: Primary 05A10
MathSciNet review: 0302459
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Abstract: Define $ f(n,j)$ as the number of binomial coefficients $ \left( {\begin{array}{*{20}{c}} n \\ r \\ \end{array} } \right)$ divisible by exactly $ {2^j}$. We find formulas for $ f(n,j)$ for $ 0 \leqq j \leqq 4$ and evaluate $ f(n,j)$ for special values of n.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0302459-9
PII: S 0002-9939(1971)0302459-9
Keywords: Binomial coefficient, composition of a positive integer
Article copyright: © Copyright 1971 American Mathematical Society