deletions | additions       diff --git a/untitled.tex b/untitled.tex  index f6fe4a3..eb2b461 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
The we can see that the powers of 2 follow a sequence $0,1,3,4,7,8,10,11,15,16,(18?)$ which is potentially A005187, the number of ones in the binary expansion of $2n$, and the denominators of the convergents of $1/\sqrt{1-x}$, we will denote this quantity $\xi(n)$, with $\xi(0)=0,\xi(1)=1,\cdots$.  It then appears that for $a_{k-m}$ the coefficent of the highest power of $(k-m)$ is $1$, the coefficent of the next highest power is $3m(m+1)/2=3,9,18,30,35,63...$. We also see the sequence $1,1,1,3,3,15,45,315,315,2835$ is A049606, the largest odd divisor of $n!$. This is very useful. We can attempt to factor $n!$ out of the coefficients.  Then, letting $\chi(n)$ be A011371, the number of binary digits in $n$, we have \begin{equation}  \kappa(n)=\frac{(-1)^n2^{n+\chi(n)-\xi(n)}}{n!}=\frac{(-1)^n}{n!} \kappa(n)=\frac{(-1)^n2^{n+\chi(n)-\xi(n)}}{n!}  \end{equation}  and  \begin{equation}