Reliable prediction of the properties of nanosystems with radical nature has been tremendously challenging for common computational approaches. Aiming to overcome this, we employ thermally-assisted-occupation density functional theory (TAO-DFT) to investigate various electronic properties (e.g., singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, symmetrized von Neumann entropy, active orbital occupation numbers, and visualization of active orbitals) associated with a series of triangle-shaped graphene nanoflakes with n fused benzene rings at each side (denoted as n-triangulenes), which can be extended from triangulene. According to our TAO-DFT results, the ground states of n-triangulenes are singlets for all the values of n studied (n = 3, 5, 7, 9, ..., and 21). Moreover, the larger the values of n, the more significant the polyradical nature of n-triangulenes. There are approximately (n - 1) unpaired electrons for the ground state of n-triangulene. The increasing polyradical nature of the larger n-triangulenes should be closely related to the fact that the active orbitals tend to be mainly concentrated at the periphery of n-triangulenes, apparently increasing with the molecular size.