Digit sums of binomial sums

Binomial Sums and Identities

Generalising Tuenter’s binomial sums

Tuenter [Fibonacci Quarterly 40 (2002), 175-180] and other authors have considered centred binomial sums of the form Sr(n) = ∑

Multiple binomial sums

Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with algebraic generating function. We study the representation of the generating functions of binomial sums by integrals of rational functions. The outcome is two...

Generalizing Tuenter’s Binomial Sums

Tuenter considered centered binomial sums of the form Sr(n) = 2n ∑

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 ]