First of, I am sorry if I am posting it in a wrong section. If so, can someone please move this thread to the appropriate section?

Now, my problem:

I have a series of the form S1=x(x+1)

and another series S1/k, for any kâˆˆN. Now I want to find the values where the elements of two series are equal. For example, let k be 3, then the intersection of the two series gives 2,30,420,5852,81510,1135290. Can a formula be derived to find these ways without resorting to equating the two series and deriving quadratic roots i.e. using series formulae or triangular numbers etc.?