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What techniques/methods can be used to prove that the sequence produced by $n\cdot (n+1)\cdot (2\cdot n+1)/6$ contains only one square ($4900$) greater than 1?
While this particular sequence is an interesting example, I'm interested in techniques that can be generalized to any sequence with a polynomial generating function.
In general, this is equivalent to asking for the solution to the Diophantine equation: $$ a^2 = n\cdot (n+1)\cdot (2\cdot n+1)/6. $$