There are infinitely polynomials of order 7 that will give these
as the first seven numbers and any one of these could be "the"
rule. There are also non-polynomial solutions. Any one of these
could be the pattern. Short of reading the mind of the person who
posed the question, there is no way of determining which of the
infinitely many solutions is the "correct" one.
The simplest solution based on a polynomial of order 6 is
t(n) = (-4*n^6 + 90*n^5 - 805*n^4 + 3660*n^3 - 8731*n^2 +
10470*n - 4320)/360 for n = 1, 2, 3, ...