6. D.

It is easy to see that the terms of this sequence are
$$
\begin{aligned}
& a_{1}=2+3, a_{2}=a_{1}+4, a_{3}=a_{2}+5, \cdots, \\
& a_{n}=a_{n-1}+(n+2) . \\
& \text { Hence } a_{n}=\frac{1}{2}(n+2)(n+3)-1 \\
\Rightarrow & a_{624}=196250 .
\end{aligned}
$$
6. As shown in Figure 1, stones are arranged in a trapezoidal shape, and the sequence of numbers formed by the "trapezoidal" structure of the stones, $\left\{a_{n}\right\}$: $5,9,14,20, \cdots$, is called the "trapezoidal sequence." According to the construction of the "trapezoid," the value of $a_{624}$ is ( ).
(A) 166247
(B) 196248
(C) 196249
(D) 196250