How to make my iterated function calculate more quickly?

Sn[n_] := x /; 0 <= n <= 8
Sn[n_] := 0 /; n > 8

Tn[n_] := 1 /; 0 <= n <= 8
Tn[n_] := 0 /; n > 8

Un[n_] := x /; 0 <= n <= 8
Un[n_] := 0 /; n > 8


Z[n_] := n^2 + n;

an[0] = 1;

an[n_] := 
  an[n] = -1/
    Z[n] Sum[((k)*(k - 1)*Sn[n - k] + (k)*Tn[n - k] + Un[n - k])*
      an[k], {k, 0, n - 1, 1}];
an[500]

Some friends say my last code was not clear,I am very sorry.Here I rewrite the code. This code calcute too slowly,please help me!Thank you!

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