Basic questions?

[Ralf Stephan]

> A108150       C(n+1,1)*C(n+3,1)

This is not an interesting sequence.

> All terms are <a square -1> so I submitted the formula a(n-1)=(n^2)-1
> verified for all terms displayed.
> 
> But I wonder:
> 1) How to be shure it is verified to the infinity?

As you rightly assume, by proving, in principle (your given proof
is correct BTW).

However, at the OEIS, people have come to agree that we can make some
assumptions, e.g.
- if we can be sure both sequences have a rational g.f., it suffices
  to compare about twice as much members as the degree of the g.f. denominator.
  I think one can prove that. (It also applies to your example)

> 2) Should we *prove* that a formula is correct for any corresponding
> sequence?

Only if you write the formula as is. If you prepend the word 'Conjecture',
then it will be clear it's not proven.
If your proof is interesting, or the formula is too complicated to put it
into the OEIS, you should write up a paper and give the reference, or an 
URL to the preprint.


ralf