Hi. Looking to solve t2 d{A(n)t}/dt = tA(n-1)t - A(n)t for Stirling number of the first kind.
Sorry but your question makes no sense, at least to me.
You posted this is the calculus form, the continuous change forum.
But Stirling numbers of the first kind are finite (discrete). Stirling numbers of the
first kind, say $\displaystyle S(n,k)$, counts the number of ways of putting n distinct objects into k indistinguishable cells.
Now can you clear up my confusion?