The reason is the following: add a `print g[k]`

after the definition of `g[k]`

, you will see the following expressions (for `len=10`

):

```
-180*x/(180*x - 1) + 1
-144*x/(144*x + 1/(180*x/(180*x - 1) - 1)) + 1
-112*x/(112*x + 1/(144*x/(144*x + 1/(180*x/(180*x - 1) - 1)) - 1)) + 1
-84*x/(84*x + 1/(112*x/(112*x + 1/(144*x/(144*x + 1/(180*x/(180*x - 1) - 1)) - 1)) - 1)) + 1
-60*x/(60*x + 1/(84*x/(84*x + 1/(112*x/(112*x + 1/(144*x/(144*x + 1/(180*x/(180*x - 1) - 1)) - 1)) - 1)) - 1)) + 1
-40*x/(40*x + 1/(60*x/(60*x + 1/(84*x/(84*x + 1/(112*x/(112*x + 1/(144*x/(144*x + 1/(180*x/(180*x - 1) - 1)) - 1)) - 1)) - 1)) - 1)) + 1
-24*x/(24*x + 1/(40*x/(40*x + 1/(60*x/(60*x + 1/(84*x/(84*x + 1/(112*x/(112*x + 1/(144*x/(144*x + 1/(180*x/(180*x - 1) - 1)) - 1)) - 1)) - 1)) - 1)) - 1)) + 1
-12*x/(12*x + 1/(24*x/(24*x + 1/(40*x/(40*x + 1/(60*x/(60*x + 1/(84*x/(84*x + 1/(112*x/(112*x + 1/(144*x/(144*x + 1/(180*x/(180*x - 1) - 1)) - 1)) - 1)) - 1)) - 1)) - 1)) - 1)) + 1
-4*x/(4*x + 1/(12*x/(12*x + 1/(24*x/(24*x + 1/(40*x/(40*x + 1/(60*x/(60*x + 1/(84*x/(84*x + 1/(112*x/(112*x + 1/(144*x/(144*x + 1/(180*x/(180*x - 1) - 1)) - 1)) - 1)) - 1)) - 1)) - 1)) - 1)) - 1)) + 1
```

So, you can see that they become quite large, so that the computation become very long, which explains why your computation is slow.

So, to check our hypothesis (and solve the problem), what you have to do is to simplify the expressions to keep something small along the computation. You can work on fraction field (very fast), or, if you want to stay in the symbolic ring, then you should replace:

```
g[k] = 1 - f(k)/(f(k)-1/g[k+1])
```

with

```
g[k] = (1 - f(k)/(f(k)-1/g[k+1])).full_simplify()
```

Now, with `len=20`

, you get without waiting:

```
[1,
4,
64,
2176,
126976,
11321344,
1431568384,
243680935936,
53725527801856,
14893509177769984,
5070334006399074304,
2079588119566033616896,
1011390382859091900891136,
575501120339508919401447424,
378784713733072451034702413824,
285539131625477547496925147693056,
244410463271028625971446390840098816,
235752874763994894181564461756568305664,
254537317950438535955585357041409084882944,
305766504814246648318888059404547150542012416]
```

.

:P

Clear the browser cache and try again :)