The equation of state of Quantum Chromodynamics (QCD) at finite density
is currently known only in a limited range in the baryon chemical potential $\mu_B$. This
is due to fundamental shortcomings of traditional methods such as Taylor expansion
around $\mu_B=0$. In this contribution, we present an alternative scheme
\cite{Borsanyi:2021sxv} that displays substantially improved convergence over the Taylor
expansion method. We calculate the alternative expansion coefficients in the
continuum, and show our results for the thermodynamic observables up to
$\mu_B/T\le3.5$.