query: Stirling numbers of second type
positive_passages.docid: 152911
positive_passages.text: Stirling numbers combinatorial proof
negative_passages.docid: 71797
negative_passages.text: Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
negative_passages.docid: 134440
negative_passages.text: An unexpected application of non-trivial combinatorics
negative_passages.docid: 14836
negative_passages.text: A polynomial sequence
negative_passages.docid: 102429
negative_passages.text: There are 2 groups of order 6 (up to isomorphism)
negative_passages.docid: 148796
negative_passages.text: Calculating $\tau(n)$, the number of positive divisors of $n \in \mathbb N$
negative_passages.docid: 103732
negative_passages.text: Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.
negative_passages.docid: 85786
negative_passages.text: Generating functions of partition numbers
negative_passages.docid: 116970
negative_passages.text: On the number divisors of a number
negative_passages.docid: 144890
negative_passages.text: Recurrence $f_{n+2}=af_{n+1}+bf_n$
negative_passages.docid: 132165
negative_passages.text: "Polynomials" with non-integer exponents
negative_passages.docid: 35660
negative_passages.text: Elements of order 2 in $D_{2n}$
negative_passages.docid: 129536
negative_passages.text: Asymptotic behaviour of sums of consecutive powers
negative_passages.docid: 19633
negative_passages.text: Closed form for a pair of continued fractions
negative_passages.docid: 39698
negative_passages.text: On uniqueness of sums of prime powers
negative_passages.docid: 140433
negative_passages.text: The number of ways of writing an integer as a sum of two squares
negative_passages.docid: 117681
negative_passages.text: For which Natural $n\ge2: \phi(n)=n/2$