Employing a high-order symplectic integrator and an adaptive time-step algorithm, we perform molecular-dynamics simulations of antihydrogen formation, in a cold plasma confined by a strong magnetic field, over time scales of microseconds. Sufficient positron-antiproton recombination events occur to allow a statistical analysis for various properties of the formed antihydrogen atoms. Giant-dipole states are formed in the initial stage of recombination. In addition to neutral atoms, we also observe antihydrogen positive ions (H(+)), in which two positrons simultaneously bind to an antiproton.