See Trappmann's overview of Kneser's results at the Tetration Forum.
The expression { n k } {\displaystyle \textstyle \left\{{n \atop k}\right\}} denotes a Stirling number of the second kind, counting the number of ways an n {\displaystyle n} -element set can be partitioned into k {\displaystyle k} blocks.
f ( x ) = χ ( x ) = ∑ n = 0 ∞ a n n ! x n {\displaystyle f(x)=\chi (x)=\sum _{n=0}^{\infty }{\frac {a_{n}}{n!}}x^{n}}
g ( x ) = e c + x − c = c ( e x − 1 ) {\displaystyle g(x)=e^{c+x}-c=c(e^{x}-1)}
f ( g ( x ) ) = ∑ n = 1 ∞ ∑ k = 1 n a k B n , k ( b 1 , … , b n − k + 1 ) n ! x n {\displaystyle f(g(x))=\sum _{n=1}^{\infty }{\frac {\sum _{k=1}^{n}a_{k}B_{n,k}(b_{1},\ldots ,b_{n-k+1})}{n!}}x^{n}}
∑ k { n k } a k c k = c a n {\displaystyle \sum _{k}\textstyle \left\{{n \atop k}\right\}\;a_{k}\;c^{k}=c\;a_{n}}
ϕ ( ϕ ( x ) ) = e x {\displaystyle \phi (\phi (x))=e^{x}}
denotes a Stirling number of the second kind, counting the number of ways an 
-element set can be partitioned into 
blocks.
