query: Stirling numbers of first order
positive_passages.docid: 24212
positive_passages.text: proving how many permutations exist.
negative_passages.docid: 78314
negative_passages.text: Generating function for the factorial sequence
negative_passages.docid: 130820
negative_passages.text: The generating function for the Fibonacci numbers
negative_passages.docid: 109599
negative_passages.text: A finite sum involving the binomial coefficients and the harmonic numbers
negative_passages.docid: 121271
negative_passages.text: Stirling's Approximation Proof
negative_passages.docid: 151384
negative_passages.text: Summation of series involving binomial coefficients and polynomial of degree at most n-1
negative_passages.docid: 122504
negative_passages.text: Factorisations of permutations
negative_passages.docid: 97720
negative_passages.text: Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$
negative_passages.docid: 135558
negative_passages.text: An inequality about Stirling numbers
negative_passages.docid: 152845
negative_passages.text: Every integer is the unique sum of a "decreasing" sequence of binomial coefficients
negative_passages.docid: 117775
negative_passages.text: Combinatorial proof of a Stirling number identity.
negative_passages.docid: 142038
negative_passages.text: Finding the number of elements of order two in the symmetric group $S_4$
negative_passages.docid: 45460
negative_passages.text: Proof verification of a number theory problem involving sequences.
negative_passages.docid: 37871
negative_passages.text: Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
negative_passages.docid: 94389
negative_passages.text: Proving formula for product of first n odd numbers
negative_passages.docid: 90957
negative_passages.text: Relation between Stirling numbers of first kind and harmonic numbers
negative_passages.docid: 30003
negative_passages.text: Proving that Order for N is Anti-symmetric