[LegionMammal978]

In fact, for that 'warmup' problem, the leading term has a base and coefficient that are roots of cubic polynomials, given in the OEIS entry. But often the coefficient will be trancendental for these sorts of problems.

[aleph_minus_one]

> But often the coefficient will be tran[s]cendental for these sorts of problems.

What makes you believe that the coefficient will be transcendental? I'd rather expect some non-trivial algebraic number (i.e. root of some polynomial with rational coefficients).