\begin{definition}[Definition:Pyramidal Number]
The '''pyramidal numbers''' are integers defined as sums of sequences of polygonal numbers as follows.
Let $\map P {k, n}$ be the $n$th $k$-gonal number.
Then the '''$n$th $k$-gonal-based pyramidal number''' $\map Y {k, n}$ is defined as:
:$\ds \map Y {k, n} = \sum_{i \mathop = 1}^n \map P {k, i}$
\end{definition}