Here given is a sequence from OEIS.
The sequence is triangle of coefficients from fractional iteration of $e^x - 1$. Few terms are:
$1, 1, 3, 1, 13, 18, 1, 50, 205, 180, 1, 201, 1865, 4245, 2700, 1, 875, 16674$
The expression of finding the sequence is also given as:
$A(n,x)$ for n-th row satisfies
$A(n,x) = \displaystyle\sum_{k=0}^{n-1} Stirling_2(n, k)A(k,x)x, A(1,x) = 1$.
I am not able to get how above expression is resulting in the given sequence.
In summation, k begins from 0, but nothing is mentioned about $A(0,x)$. I assumed it to be $0$, but still can't get the above values.
Please explain how the first few terms are resulting from the expression.