The recent discovery of bulk superconductivity in trilayer nickelate ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ under high pressure is attracting a new wave of research interest. In this Letter, we study its electronic band structure and construct a minimal trilayer tight-binding model in terms of the nickel $3d_{x^2-y^2}$ and $3d_{3z^2-r^2}$ orbitals, and investigate the superconducting mechanism due to local Coulomb interactions by the unbiased functional renormalization group. We find antiferromagnetic correlations between the outer layers instead of neighboring ones, apart from the in-plane correlations. The effective interaction induces Cooper pairing with the $s_{\pm }$-wave symmetry, which changes sign across the Fermi pockets. In addition, we find the $T_c$ in ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ is systematically lower than that in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, but electron doping can further enhance $T_c$.

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• Pairing mechanisms
• Superconducting order parameter
• Unconventional superconductors
• Density functional calculations
• Functional renormalization group