Ammonium nitrate can blow up in either of two ways:

1) the more commonly known use of ammonium nitrate as an oxidizer for a fuel. This is how mining companies and blasting operations use AN, plus diesel fuel, in what is known as "ANFO" (ammonium nitrate-fuel oil") or "prill." The local coal mines here in Wyoming drill holes into a top of a bench in a pit that they want to loosen up for the dragline or shovels, and then they use a combination of prill and primers to fill the holes, which are them backfilled, and then and shot.  Here's a video showing the whole process:

https://www.youtube.com/watch?v=P8VTWqTI154

ANFO was indeed used at OKC.

2) OK, it's obvious that ammonium nitrate and a fuel oil (whether it's diesel, kerosene, crankcase oil, etc) makes a nice "boom." What isn't well known is that ammonium nitrate is quite capable of exploding without any fuel - ie, pure ammonium nitrate, often thought to be safe because there's no "fuel" for it to oxidize, can make large explosions quite well without fuel. This happens if the AN is heated to the point of "thermal decomposition," and then the ammonium nitrate basically "disassembles" into much smaller components, letting off a violent exothermic explosion that produces a great deal of oxides of nitrogen and water vapor. Here's an example of this happening, and you get to see just how violent this can be, from the explosion several years back of stored ammonium nitrate in the harbor of Beirut, Lebanon:

https://www.youtube.com/watch?v=DwRF5liTGB4

OK, when this video starts, we can see that there's a big fire on the wharf storage, and then there's a large explosion at about 0:11, and you see a violent, brown/red cloud blow up vertically. This is a cloud of oxides of nitrogen. Then at 0:13, you see this huge cloud of water vapor/steam blow outwards, which is the other byproduct of ammonium nitrate undergoing "thermal decomp." Then the shock wave hits the boat.

Now, let's talk about ammonium nitrate and "thermal decomposition:" all that is required to start ammonium nitrate to start decomposing violently is to heat it to over 200C. At some temperatures above 200C, the mode of decomposition changes, and this changes the amount of energy generated by the decomp, intermediate products, volume of end products (and therefore the pressure wave), but none of the modes of thermal decomposition are good to be near when they happen. 

Here's a detailed paper reviewing the various modes of decomposition of ammonium nitrate under heating:

https://www.researchgate.net/publication/263578419_Review_on_Thermal_Decomposition_of_Ammonium_Nitrate

For the chemical formulas of decomp, please see Table 2, formulas (2) through (6). These happen under different heating temperatures and conditions, which are explained in the paragraph immediately preceding Table 2.

So, net:net: If you respond to a fire near a large amount of stored ammonium nitrate fertilizer, approach with caution, because basic fire and heating can cause a violent explosion of ammonium nitrate, without any fuel oil or added hydrocarbon content usually used in making ANFO.