  In this note we introduce the concept of a shuffle product $\sq$ for planar
tree polynomials and give a formula to compute the planar shuffle product $S \
\sq T$ of two finite planar reduced rooted trees $S, T.$
  It is shown that $\sq$ is dual to the co-addition $\Delta$ which leads to a
formula for the coefficients of $\Delta(f).$
  It is also proved that $\Delta(EXP) = EXP {\hat \otimes} EXP$ where $EXP$ is
the generic planar tree exponential series, see [G]. Systems of quadratic
relations for the coefficients of EXP are derived.
