The Combinatorial Identity on the Jacobian Conjecture

The multidimensional sum with polynomial coefficients is computed with the help of the method of integral representation and computation of combinatorial sums. This sum was obtained in the attempt to prove the well known Jacobian conjecture (two-dimensional case). Supported in part by the Natural Sciences and Engineering Research Council of Canada on Grant NSERC-108343 and the Russian Fund of Fundamental Researches.Mathematics Subject Classifications (2000) combinatorics, algebra.