query: Why do the factorials appear in differences of consecutive powers?
positive_passages.docid: 43499
positive_passages.text: Repeatedly taking differences on a polynomial yields the factorial of its degree?
negative_passages.docid: 66364
negative_passages.text: Why is $(\sqrt{2}+\sqrt{3})^{2008}$ so close to an integer?
negative_passages.docid: 95702
negative_passages.text: Remarkable/unexpected rational numbers
negative_passages.docid: 123117
negative_passages.text: Is it possible to find $n-1$ consecutive composite integers
negative_passages.docid: 11998
negative_passages.text: In how many sequences of length $n$, the difference between every 2 adjacent elements is $1$ or $-1$?
negative_passages.docid: 23270
negative_passages.text: The sum of powers of two and two's complement – is there a deeper meaning behind this?
negative_passages.docid: 89413
negative_passages.text: Can there be only one extension to the factorial?
negative_passages.docid: 73102
negative_passages.text: Given the factors of $N$, is there a method for computing the factors of $N-1$ or $N+1$?
negative_passages.docid: 152870
negative_passages.text: Near integers in powers of binomials with radicals
negative_passages.docid: 158114
negative_passages.text: Representing the double factorial of LaguerreL[n, 1, x]/( (n + 1) LaguerreL[n, 0, x])
negative_passages.docid: 46751
negative_passages.text: Power rule step. Where does equation of the difference of two numbers raised to the same power come from?
negative_passages.docid: 145582
negative_passages.text: $\sum (-1)^n/n$ fails the p-series test, but passes the alternating series test?
negative_passages.docid: 142730
negative_passages.text: Superscripts appear in various weird places in fractions
negative_passages.docid: 81502
negative_passages.text: Getting different output from seemingly identical calculations
negative_passages.docid: 102524
negative_passages.text: $ 1^k+2^k+3^k+...+(p-1)^k $ always a multiple of $p$?
negative_passages.docid: 124116
negative_passages.text: What does the notation $\binom{n}{i}$ mean?
negative_passages.docid: 120913
negative_passages.text: How would you write a non-recursive algorithm to calculate factorials?