implementing gaussian filter in C

I know due to the central limit theorem the Gaussian filter can be simplified to a weighted moving average.

I'm still understanding signals, but I know a moving average is

Y [ i ] = $\frac{1}{N}$$\sum ^{N-1}_{j=0}$ X[ i + j ]

From Wiki on Gaussian filter, if I process through a moving average for 4 or more times, it is an approximate of the Gaussian.

How would I do this ? I figured it would be some recursion, but any explanation?
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