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Numerators of the convergents to x = 1/(x^4+1).
0

%I #5 Oct 01 2013 21:35:26

%S 1,1,16,83521,493639046268679584001

%N Numerators of the convergents to x = 1/(x^4+1).

%C These numbers are quartics. The recursion provides a method of solving the quintic x^5 + x - 1. In general, extending this notion, we can use the recursion x = 1/(x^(n-1)+1) to find a solution for n-th degree equations of the form x^n+x-1=0.

%o (PARI) x=0;for(j=1, 7, x=1/(x^4+1); print1((numerator(x))", "))

%K frac,nonn

%O 0,3

%A _Cino Hilliard_, Sep 21 2008