  It is believed arXiv:0808.2762, arXiv:math/9904055 that, among the
coefficients entering Kontsevich's formality quasi-isomorphism
arXiv:q-alg/9709040, there are irrational (possibly even transcendental)
numbers. In this paper, we prove that a formality quasi-isomorphism for
Hochschild cochains of a polynomial algebra over rationals can be constructed
recursively. The proof that the proposed recursive algorithm works, is based on
the existence of formality quasi-isomorphism over reals. However, the algorithm
requires no explicit knowledge of the coefficients entering Kontsevich's
construction. Although this algorithm completely bypasses Tamarkin's approach
arXiv:math/0003052, arXiv:math/9803025, the construction is inspired by
Proposition 5.8 from the classical paper (Algebra i Analiz, 1990) by V.
Drinfeld.
