The missing character is 240.
The sequence is a list of numbers that are the sum of the first $n$ perfect squares, where $n$ is the number of digits in the number. For example, the first number in the sequence is 1 because it is the sum of the first perfect square, 1. The second number in the sequence is 4 because it is the sum of the first two perfect squares, 1 and 4. The third number in the sequence is 9 because it is the sum of the first three perfect squares, 1, 4, and 9.
The number of digits in 84 is 2, so the first two perfect squares that need to be added are 1 and 4. The sum of 1 and 4 is 5, which is not in the sequence.
The number of digits in 195 is 3, so the first three perfect squares that need to be added are 1, 4, and 9. The sum of 1, 4, and 9 is 14, which is not in the sequence.
The number of digits in 240 is 4, so the first four perfect squares that need to be added are 1, 4, 9, and 16. The sum of 1, 4, 9, and 16 is 30, which is in the sequence.
The number of digits in 265 is 5, so the first five perfect squares that need to be added are 1, 4, 9, 16, and 25. The sum of 1, 4, 9, 16, and 25 is 55, which is not in the sequence.
Therefore, the missing character is 240.