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%I #8 Sep 08 2022 08:46:09
%S 1,2,2,6,-6,-42,378,8694,-356454,-31011498,5240943162,1797643504566,
%T -1224195226609446,-1673474874775112682,4566912933261282509178,
%U 24949045354406386347639414,-272468524315472145302570040294,-5952619850720119958425247670303018
%N a(n) = 5 * a(n-1) - 2 * a(n-1)^2 / a(n-2), with a(0) = 1, a(1) = 2.
%H G. C. Greubel, <a href="/A247525/b247525.txt">Table of n, a(n) for n = 0..83</a>
%F 0 = a(n)*(-5*a(n+1) + a(n+2)) + a(n+1)*(+2*a(n+1)) for all n in Z.
%F a(n+1) = a(n) * A140966(n) for all n in Z.
%t RecurrenceTable[{a[n] == 5*a[n - 1] - 2*a[n - 1]^2/a[n - 2], a[0] == 1, a[1] == 2}, a, {n, 0, 50}] (* _G. C. Greubel_, Aug 05 2018 *)
%o (PARI) {a(n) = if( n<0, 1 / prod(k=1, -n, (5 + (-2)^-k) / 3), prod(k=0, n-1, (5 + (-2)^k) / 3))};
%o (Magma) I:=[1, 2]; [n le 2 select I[n] else 5*Self(n-1) - 2*Self(n-1)^2/Self(n-2): n in [1..30]]; // _G. C. Greubel_, Aug 05 2018
%Y Cf. A140966.
%K sign
%O 0,2
%A _Michael Somos_, Sep 18 2014