Stirling Number of the first type:
\[S(n,m)=S(n-1,m-1)+(n-1)*s(n-1,m)\]
\[n!=\sum_{i=0}^nS(n,i)\]
Stirling Number of the second kind:
\[S(n,m)=S(n-1,m-1)+m*S(n-1,m)\]
\[S(n,m)=\frac{\sum_{k=0}^m(−1)^kC(m,k)(m−k)^n}{m!}\]
\[m^n=\sum_{i=0}^{min(m,n)}S(n,i)*i!*C(m,i)\]
\[S(n,m)=\sum_{k=0}^m\frac{(−1)^k}{k!}\frac{(m−k)^n}{(m−k)!}\]
Wrong row problem
\[D(n)=(n-1)(D(n-1)+D(n-2))\]
Full re-arrangement
\ (a [i] \) for the same number of
\[\frac{(\sum a_i)!}{\Pi(a_i)!}\]
Decline in power
\[x^{\underline{k}}=x*(x−1)*(x−2)...*(x-k+1)\]
pending upgrade