Doubly triangular number

In mathematics, the doubly triangular numbers are the numbers that appear within the sequence of triangular numbers, in positions that are also triangular numbers. That is, if ${\displaystyle T_{n}=n(n+1)/2}$ denotes the ${\displaystyle n}$th triangular number, then the doubly triangular numbers are the numbers of the form ${\displaystyle T_{T_{n}}}$.