Thom series for the singularity A7

Determine the Thom series Ts(A_7) for the contact singularity A_7 (local algebra C[x]/(x^8)), i.e., construct a formal series Ts(A_7) in variables d_i such that for every integer ℓ ≥ 0 the Thom polynomial Tp(A_7,ℓ) is obtained by the substitution d_i = c_{i+ℓ+1}.

Background

Thom series unify the Thom polynomials Tp(η,ℓ) across all relative dimension differences ℓ via a single formal series in shifted variables and are known for many singularities (e.g., A_2, A_3).

The author notes a significant gap: even for the classical Morin family, the Thom series for A_7 remains undetermined.