query: sum of multiplications of number sets with sum n
positive_passages.docid: 142978
positive_passages.text: combinatorics: sum of product of integer compositions
negative_passages.docid: 99530
negative_passages.text: Algorithm to multiply nimbers
negative_passages.docid: 74058
negative_passages.text: Sums and products of algebraic numbers
negative_passages.docid: 19571
negative_passages.text: Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
negative_passages.docid: 1627
negative_passages.text: Cartesian product of an arbitrary number of sets
negative_passages.docid: 94060
negative_passages.text: Sum of square binomial coefficients
negative_passages.docid: 81124
negative_passages.text: Infinite product problem: $\sum p_n0$
negative_passages.docid: 72402
negative_passages.text: Summation of natural number set with power of $m$
negative_passages.docid: 21000
negative_passages.text: Calculating $\sum_{k=1}^nk(k!)$ combinatorially
negative_passages.docid: 53312
negative_passages.text: Multiplication principle and permutation
negative_passages.docid: 25338
negative_passages.text: Sum of $n$ integers from set of size $2n-1$ divides $n$
negative_passages.docid: 44577
negative_passages.text: Finding a formula to sum natural numbers up to $n$
negative_passages.docid: 147766
negative_passages.text: Sum of Permutations from 0 to n
negative_passages.docid: 36486
negative_passages.text: Finding the total number of set-bits from 1 to n
negative_passages.docid: 112644
negative_passages.text: The product of two numbers that can be written as the sum of two squares
negative_passages.docid: 152638
negative_passages.text: The set of integers $n$ expressible as $n=x^2+xy+y^2$
negative_passages.docid: 92784
negative_passages.text: Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$