Lindeberg's Condition is not necessary

Question

Let $X_n^k$ be Triangular Array ($k\leq n$) of independent mean $0$ random variables. Suppose $\sum_k^n \text{Var}(X_n^k) = 1$.

Lindeberg's Condition \begin{equation} \lim_{n\to\infty} \sum_k^n E({X_n^k}^2;|X_n^k| > \epsilon) = 0 \quad\text{implies}\quad \sum_k^n X_n^k \Rightarrow_D N(0,1) \end{equation}

Question Show that Lindeberg's Condition is not necessary.

Only example that I was able to write down is $X_1 = N(0,1)$ and $X_2\equiv 0, X_3\equiv 0 ,\dots$.
Is there an example of non-degenerate sequence of random variables which does not satisfy Lindeberg's Condition but still converge in distribution to normal distribution?

It might be a duplicate, but I couldn't find it.