Step 1: Look for a pattern in the sequence.
We observe that:
$1 = 1^2$
$4 = 2^2$
$9 = 3^2$
$16 = 4^2$
$36 = 6^2$
$49 = 7^2$
All numbers except $19$ are perfect squares of natural numbers.
Step 2: Since $19$ is not a perfect square, it does not fit the pattern.
Thus, the odd one out is $\mathbf19$.