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%I #20 Aug 19 2020 03:59:22
%S 1,-2,3,-2,-1,4,-6,6,-3,-2,9,-16,17,-10,-5,24,-36,36,-21,-10,46,-74,
%T 77,-42,-22,94,-144,142,-78,-38,172,-266,266,-146,-73,312,-471,464,
%U -251,-122,534,-814,801,-432,-213,910,-1364,1328,-713,-344,1485,-2234,2178
%N Expansion of square of continued fraction 1/ ( 1+q/ ( 1+q^2/ ( 1+q^3/ ( 1+q^4/... )))).
%H Seiichi Manyama, <a href="/A055101/b055101.txt">Table of n, a(n) for n = 0..10000</a>
%H For the third power see G. E. Andrews, <a href="http://www.jstor.org/stable/2974472">Simplicity and surprise in Ramanujan's "Lost" Notebook</a>, Amer. Math. Monthly, 104 (No. 10, Dec. 1997), 918-925.
%F a(0) = 1, a(n) = -(2/n)*Sum_{k=1..n} A109091(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 16 2017
%F Euler transform of period 5 sequence [-2, 2, 2, -2, 0, ...]. - _Georg Fischer_, Aug 18 2020
%Y See A007325 for first power (which has an alternative g.f.), A055102 for cube, A055103 for 4th power.
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_, Jun 14 2000
%E More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 20 2000
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