330

Number
$330$ (three hundred and thirty) is:


 * $2 \times 3 \times 5 \times 11$


 * The $15$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $51$, $70$, $92$, $117$, $145$, $176$, $210$, $247$, $287$:
 * $330 = \displaystyle \sum_{k \mathop = 1}^{15} \left({3 k - 2}\right) = \dfrac {15 \left({3 \times 15 - 1}\right)} 2$


 * The $29$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $222$, $247$, $260$, $287$, $301$:
 * $330 = \dfrac {15 \left({3 \times 15 - 1}\right)} 2$


 * The $8$th pentatope number after $1$, $5$, $15$, $35$, $70$, $126$, $210$:
 * $330 = \displaystyle \sum_{k \mathop = 1}^8 \dfrac {k \left({k + 1}\right) \left({k + 2}\right)} 6 = \dfrac {8 \left({8 + 1}\right) \left({8 + 2}\right) \left({8 + 3}\right)} {24}$