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A247540 a(n) = 2*a(n-1) - 3*a(n-1)^2 / a(n-2), with a(0) = a(1) = 1.

%I A247540 #11 Sep 08 2022 08:46:09
%S A247540 1,1,-1,-5,65,2665,-322465,-117699725,128645799425,422086867913425,
%T A247540 -4153756867136015425,-122639671502190855423125,
%U A247540 10862563623963550637392450625,2886411268723218638918559372525625,-2300934493386669693418957707961899750625
%N A247540 a(n) = 2*a(n-1) - 3*a(n-1)^2 / a(n-2), with a(0) = a(1) = 1.
%H A247540 Reinhard Zumkeller, <a href="/A247540/b247540.txt">Table of n, a(n) for n = 0..60</a>
%F A247540 0 = a(n)*(-2*a(n+1) + a(n+2)) + a(n+1)*(+3*a(n+1)) for all n in Z.
%F A247540 a(n+1) = a(n) * (-1)^n * A046717(n) for all n in Z.
%F A247540 a(1-n) = (-3)^(n*(n-1)/2) / a(n) for all n in Z.
%t A247540 RecurrenceTable[{a[n] == 2*a[n-1] - 3*a[n-1]^2/a[n-2], a[0]==1, a[1]==1}, a, {n,0,30}] (* _G. C. Greubel_, Aug 04 2018 *)
%o A247540 (PARI) {a(n) = if( n<0, 1 / prod(k=1, -n, (1 + (-3)^-k) / 2), prod(k=0, n-1, (1 + (-3)^k) / 2))};
%o A247540 (Haskell)
%o A247540 a247540 n = a247540_list !! n
%o A247540 a247540_list = 1 : 1 : zipWith (-)
%o A247540    (map (* 2) xs) (zipWith div (map ((* 3) . (^ 2)) xs) a247540_list)
%o A247540    where xs = tail a247540_list
%o A247540 -- _Reinhard Zumkeller_, Sep 20 2014
%o A247540 (Magma) I:=[1, 1]; [n le 2 select I[n] else 2*Self(n-1) - 3*Self(n-1)^2/Self(n-2): n in [1..30]]; // _G. C. Greubel_, Aug 04 2018
%Y A247540 Cf. A046717.
%K A247540 sign
%O A247540 0,4
%A A247540 _Michael Somos_, Sep 18 2014