[A033452]

[Floor en Lyanne van Lamoen]

Thanks. Apologies for asking such a simple question. I had a misfit in
offsets in the formulae I used - Benoit Cloitre helped me out. This also
makes it clear very easily.

Floor.

Christian G. Bower wrote:
> 
> Floor en Lyanne van Lamoen <f.v.lamoen at wxs.nl> wrote:
> > Purely by calculation it seems that A033452(n) = A005493(n)-A000110(n+1)
> > - can somebody understand why this is indeed true?
> >
> > Floor.
> >
> 
> A033452 is Stirling transform of n^2
> 
> n^2 has egf e^x * (x^2+x)
> A033452 thus has egf e^(e^x-1) * ( (e^x-1)^2 + (e^x-1) )
> which simplifies to e^(e^x-1) * (e^2x - e^x)
> 
> A005493 has egf e^(e^x+2x-1)
> A000110 has egf e^(e^x-1)
> A000110(n+1) has as egf derivative of A000110 which is e^(e^x+x-1)
> 
> work out the arithmetic and you'll see they are the same.
> 
> Christian