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%I #14 Jun 13 2016 13:18:36
%S 1,0,0,1,4,12,36,116,392,1350,4696,16500,58572,209824,757440,2752185,
%T 10057636,36943044,136319052,505086728,1878395920,7009239644,
%U 26235435248,98475145476,370584275964,1397918543552,5284861554816
%N Number of bracketings of 0#0#0#...#0 giving result 0, where 0#0 = 0#1 = 1#0 = 1, 1#1 = 0.
%C Operation # can be interpreted as NOT AND. The ratio a(n)/A000108(n-1) converges to (2-sqrt(2))/2. Thanks to Soren Galatius Smith
%H G. C. Greubel, <a href="/A055395/b055395.txt">Table of n, a(n) for n = 1..500</a>
%F G.f.: 1 - (1/2)*(1 - 4*x)^(1/2) - (1/2)*(3 - 2*(1 - 4*x)^(1/2) - 4*x)^(1/2).
%F G.f.: (1 + 2*C(x) - sqrt(1 + 4*C(x)^2))/2, where C(x) = (1 - sqrt(1 - 4*x))/2 is the g.f. of the Catalan numbers (A000108). - _Paul D. Hanna_, Jun 10 2016
%F G.f. A(x) satisfies: A(x) = x + (A(x) - C(x))^2, where C(x) = x + C(x)^2 is a g.f. of the Catalan numbers (A000108). - _Paul D. Hanna_, Jun 11 2016
%t f[x_] := (1 - Sqrt[1 - 4*x])/2; CoefficientList[Series[(1 + 2*f[x] - Sqrt[1 + 4*(f[x])^2])/(2*x), {x, 0, 50}], x] (* _G. C. Greubel_, Jun 10 2016 *)
%Y Cf. A055113, A055392, A273958.
%K nonn
%O 1,5
%A _Jeppe Stig Nielsen_, Jun 24 2000
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