Sums of derivatives of binomial coefficients
نویسندگان
چکیده
منابع مشابه
On Sums of Binomial Coefficients
In this paper we study recurrences concerning the combinatorial sum [n r ] m = ∑ k≡r (mod m) (n k ) and the alternate sum ∑ k≡r (mod m)(−1) (n k ) , where m > 0, n > 0 and r are integers. For example, we show that if n > m−1 then b(m−1)/2c ∑ i=0 (−1) (m− 1− i i )[n− 2i r − i ]
متن کاملSums of Reciprocals of Triple Binomial Coefficients
Recommended by George Andrews We investigate the integral representation of infinite sums involving the reciprocals of triple bino-mial coefficients. We also recover some wellknown properties of ζ3 and extend the range of results given by other authors.
متن کاملSums Involving the Inverses of Binomial Coefficients
In this paper, we compute certain sums involving the inverses of binomial coefficients. We derive the recurrence formulas for certain infinite sums related to the inverses of binomial coefficients.
متن کاملCongruences for Sums of Binomial Coefficients
Let m > 0 and q > 1 be relatively prime integers. We find an explicit period ν m (q) such that for any integers n 0 and r we have n + ν m (q) r m (a) ≡ n r m (a) (mod q), provided that a = −1 and n = 0, or a is an integer with 1 − (−a) m relatively prime to q, where n r m (a) = k≡r (mod m) n k a k. This is a further extension of a congruence of Glaisher.
متن کاملCertain Binomial Sums with Recursive Coefficients
In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving binomial coefficients and Fibonacci type sequences.
متن کاملذخیره 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: Advances in Applied Mathematics
سال: 2009
ISSN: 0196-8858
DOI: 10.1016/j.aam.2008.07.001