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%I #2 Mar 30 2012 18:37:23
%S 1,1,1,3,28,658,36336,4918960,1913308480,2722820397008,
%T 16147361055588096,383879833447290828032,34790330152647391683716096,
%U 11818617432918372433417869737472
%N G.f. satisfies: A(x) = 1 + x*Sum_{n>=0} log( A(2^n*x) )^n/(2^n*n!).
%F a(n+1) = [x^n] A(x)^(2^(n-1)) for n>=0, with a(0)=1, where A(x) = Sum_{n>=0} a(n)*x^n.
%e G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 28*x^4 + 658*x^5 + 36336*x^6 +...
%e A(x) = 1 + x*[1 + log(A(2x))/2 + log(A(4x))^2/(4*2!) + log(A(8x))^3/(8*3!) + log(A(16x))^4/(16*4!) +...].
%e Coefficients in the 2^n-th powers of A(x) begin:
%e A^(2^0)=[1,(1), 1, 3, 28, 658, 36336, 4918960, 1913308480,...];
%e A^(2^1)=[1, 2,(3), 8, 63, 1378, 74053, 9912076, 3836532284,...];
%e A^(2^2)=[1, 4, 10,(28), 167, 3056, 154060, 20129640, 7713183207,...];
%e A^(2^3)=[1, 8, 36, 136,(658), 8008, 336692, 41562232, 15590683759,...];
%e A^(2^4)=[1, 16, 136, 848, 4788,(36336), 867384, 89267088,...];
%e A^(2^5)=[1, 32, 528, 6048, 55208, 456544,(4918960), 224294304,...];
%e A^(2^6)=[1, 64, 2080, 45888, 776272, 10833088, 133934688,(1913308480), ...]; ...
%e where the diagonal terms in parenthesis form this sequence (shift left).
%o (PARI) {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, Vec(Ser(A)^(2^(#A-2)))[ #A])); A[n+1]}
%Y Cf. A132695, A181444.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Nov 03 2010
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