[seqfan] Inversion Formula for Peculiar G.F. - Help

[Ralf Stephan]

> What is the non-recursive inversion of the equation:
>  
> F(x) = (1-x) + a(1)*x*(1-x)(1-2x) + a(2)*x^2*(1-x)(1-2x)(1-3x) + ...
>              + a(n)*x^n*(1-x)(1-2x)(1-3x)*..*(1-(n+1)x) + ...
>  
> Knowing F(x), can one determine a(n) without recursion?

If so, this may not be too important. G.f.s of bifurcative ('divide-and-
conquer') sequences are resulting from Mahler-type functional equations,
and resolving the recursion iteratively gets you g.f.s with infinite sums. 
That does not help with asymptotics which, as Valery Liskovets remarked,
is what the folks out there need.


ralf