[A033452]

[Christian G. Bower]

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