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%I
%S 1,1,3,9,32,122,490,2044,8769,38455,171606,776763,3557681,16457402,
%T 76778667,360830164,1706641162,8117569255,38804142203,186323145806,
%U 898247214881,4346078073871,21097315227638,102721050351404,501515949459113,2454747530072567,12043165949629976
%N G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n * A(x)^A026255(n).
%C Sequence A026255 is a self-inverse permutation of the natural numbers where
%C A026255([k*sqrt(3)]) = [k*(3+sqrt(3))/2] and
%C A026255([k*(3+sqrt(3))/2]) = [k*sqrt(3)] for k>=1, and [x] = floor(x).
%F G.f. satisfies: A(x) = 1 + Sum_{n>=1} A(x)^n * x^A026255(n).
%e G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 32*x^4 + 122*x^5 + 490*x^6 +...
%e where A(x) = 1 + x*A(x)^2 + x^2*A(x) + x^3*A(x)^4 + x^4*A(x)^3 + x^5*A(x)^7 + x^6*A(x)^9 + x^7*A(x)^5 + x^8*A(x)^11 + x^9*A(x)^6 + x^10*A(x)^14 +...
%e which also equals: A(x) = 1 + A(x)*x^2 + A(x)^2*x + A(x)^3*x^4 + A(x)^4*x^3 + A(x)^5*x^7 + A(x)^6*x^9 + A(x)^7*x^5 + A(x)^8*x^11 + A(x)^9*x^6 + A(x)^10*x^14 +...
%e In the above series, the exponents begin:
%e A026255 = [2,1,4,3,7,9,5,11,6,14,8,16,18,10,21,12,23,13,26,28,15,30...].
%o (PARI) {a(n)=local(A=1+x,s=sqrt(3),t=(3+sqrt(3))/2);for(i=1,n,A=1+sum(m=1, n, x^floor(m*s)*(A+x*O(x^n))^floor(m*t)+ x^floor(m*t)*(A+x*O(x^n))^floor(m*s))); polcoeff(A, n)}
%Y Cf. A193620.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 01 2011
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