query: Stirling numbers of the first kind identity
positive_passages.docid: 27585
positive_passages.text: Combinatorial proof of Stirling Number Identity (First Kind)
negative_passages.docid: 27141
negative_passages.text: Combinatorics identity question
negative_passages.docid: 96919
negative_passages.text: Characteristic equation of a recurrence relation
negative_passages.docid: 115686
negative_passages.text: A finite summation of double binomial coefficients
negative_passages.docid: 147425
negative_passages.text: Prove the von Staudt-Clausen congruence of the Bernoulli numbers
negative_passages.docid: 20317
negative_passages.text: Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
negative_passages.docid: 126161
negative_passages.text: Interesting property of finite integer sequence with sum 1
negative_passages.docid: 90904
negative_passages.text: Combinatorial proof of an identity with squared binomial coefficients
negative_passages.docid: 31076
negative_passages.text: Roots of unity filter, identity involving $\sum_{k \ge 0} \binom{n}{3k}$
negative_passages.docid: 86194
negative_passages.text: Infinite series with the binomial coefficient
negative_passages.docid: 137215
negative_passages.text: Cesaro identity for Fibonacci numbers: $ F_{2n} = \sum_{k=1}^n \binom{n}{k} F_k$
negative_passages.docid: 113068
negative_passages.text: Identity of moment-generating functions
negative_passages.docid: 39724
negative_passages.text: Combinatorial Identities
negative_passages.docid: 147639
negative_passages.text: Exponential generating function with Stirling numbers
negative_passages.docid: 144571
negative_passages.text: A conjecture including binomial coefficients
negative_passages.docid: 110403
negative_passages.text: How to write Stirling numbers of the second kind?
negative_passages.docid: 145524
negative_passages.text: Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths