Solve the programming task below in a Python markdown code block.
Given a string, you progressively need to concatenate the first letter from the left and the first letter to the right and "1", then the second letter from the left and the second letter to the right and "2", and so on.

If the string's length is odd drop the central element.

For example:
```python
char_concat("abcdef")    == 'af1be2cd3'
char_concat("abc!def")   == 'af1be2cd3' # same result
```
Also feel free to reuse/extend the following starter code:
```python
def char_concat(word):
```