  The two dimensional one component plasma 2dOCP is a classical system
consisting of $N$ identical particles with the same charge $q$ confined in a
two dimensional surface with a neutralizing background. The Boltzmann factor at
temperature $T$ may be expressed as a Vandermonde determinant to the power
$\Gamma=q^2/(k_B T)$. Several statistical properties of the 2dOCP have been
studied by expanding the Boltzmann factor in the monomial basis for even values
of $\Gamma$. In this work, we use this formalism to compute the energy of the
2dOCP on a sphere. Using the same approach the entropy is computed. The entropy
as well as the free energy in the thermodynamic limit have a universal
finite-size correction term $\frac{\chi}{12}\log N$, where $\chi=2$ is the
Euler characteristic of the sphere. A non-recursive formula for coefficients of
monomial functions expansion is used for exploring the energy as well as
structural properties for sufficiently large values of $\Gamma$ to appreciate
the crystallization features for $N=2,3,\ldots,9$ particles. Finally, we make a
brief comparison between the exact and numerical energies obtained with the
Metropolis method for even values of $\Gamma$.
