  The aim of this study is to find universal critical values of the
dimensionless effective coupling constant $g_6$ and refined universal values
$g_4$ for Heisenberg ferromagnets with $n$-component order parameters. These
constants appear in the equation of state and determine the nonlinear
susceptibilities $\chi_4$ and $\chi_6$ in the critical region. The sextic
coupling $g_6$ is calculated as a function of $g_4$ in the three-loop
approximation, the series obtained is resummed by the Pade-Borel method and
then by substituting the Wilson fixed point coordinate $g_4^*$ into resultant
expression numerical values of $g_6^*$ are obtained for different $n$. The
numbers $g_4^*$ were determined from the six-loop expansions for $\beta$
function resummed using Borel-transformation-based techniques. The analysis of
the accuracy of these $g_6^*$ values showed that they differ from the true
values by no more than 1.6 %. The values of $g_6^*$ thus found were compared
also with those given by the $1/n$ method what allowed to estimate the level of
accuracy of this method.
