[seqfan] Euler transform without generating functions

[Андрей Заболотский]

Dear SeqFans,
 
How can I explain the formula for the Euler transform (relating, say, the number of graphs on n vertices to the number of connected graphs on n vertices) without using generating functions?
More here:  https://math.stackexchange.com/questions/4494715/euler-transform-without-generating-functions
I will appreciate your answers by email or at StackExchange.
 
 
Best Regards,
Andrey Zabolotskiy