Is there software that can recognize the logical link between sequence numbers?
Example 1: $\begin{array}{|l|c|c|c|c|c|c} \hline \text{sequence} & 2 & 6 & 12 & 20 & 30 & \cdots \\ \hline n & 1 & 2 & 3 & 4 & 5 & \cdots \\ \hline \end{array}$ Here the $n$th term of the sequence is $n(n+1)$.
Example 2:
$\begin{array}{|l|c|c|c|c|c|c|c} \hline \text{sequence} & 2 & 8 & 24 & 64 & 160 & 384 & \cdots \\ \hline n & 1 & 2 & 3 & 4 & 5 & 6 & \cdots \\ \hline \end{array}$ Here the $n$th term of the sequence is $n 2^n$.
Thank you.