On the Cardinality of the 𝑇₀-Topologies on a Finite Set

Table 2

𝑘	𝑇^20(𝑛,𝑘)
5⋅2^𝑛−4	𝑛^2+41𝑛−23436(𝑛)6
5⋅2^𝑛−4+2^𝑛−8	𝑛^2−11𝑛+214720(𝑛)8
5⋅2^𝑛−4+2^𝑛−7	𝑛^2−10𝑛+66120(𝑛)7
5⋅2^𝑛−4+2^𝑛−6	𝑛^2+15𝑛−8424(𝑛)6
5⋅2^𝑛−4+2^𝑛−5	𝑛^2−2𝑛−146(𝑛)5
5⋅2^𝑛−4+2^𝑛−𝑖, 𝑖=9,…,𝑛	𝑛−3(𝑖−2)!(𝑛)𝑖+1
5⋅2^𝑛−4+3⋅2^𝑛−𝑖, 𝑖=6,…,𝑛	2(𝑖−4)!(𝑛)𝑖
5⋅2^𝑛−4+5⋅2^𝑛−7	56(𝑛)7
5⋅2^𝑛−4+5⋅2^𝑛−𝑖, 𝑖=8,…,𝑛	2(𝑖−4)!(𝑛)𝑖