Consider a soccer league consisting of `n` teams. In a season, each team plays against any other team once. Clearly, there are `\frac{1}{2}(n^2-n)` games in a season. The rule is that for each match, the winning team gets 3 points and both the teams get 1 point if they tie.
`a(n)` is the number of all the possible final standings of a soccer league consisting of `n` teams.
For example, `a(2)=3` because there are `3` possible standings for a two-team league: `\{3,0\}`, `\{1,1\}`, `\{0,3\}`.
Find `a(n)`.