  Thom polynomial describes the cohomology class Poincar\'e dual to the locus
of particular singularity of a generic holomorphic map. In this paper we derive
a closed formula for the generating function of its coefficients. The method is
based on a new construction of the embedding space of punctual Hibert scheme
that we call the non-associative Hilbert scheme. The efficiency of the method
is demonstrated on explicit computation of a number of Thom polynomials,
including those associated with singularities of Thom-Boardman
types~$\Sigma^{i,j}$, $\Sigma^{2,1,1}$, $\Sigma^{2,2,1}$, and~$\Sigma^{2,2,2}$.
