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%I #4 Mar 30 2012 18:37:22
%S 1,2,-12,56,-12080,-9802944,-31002027840,-344291147482368,
%T -13751106868604649216,-2036529273026085671952640,
%U -1148515664060697951003807202304
%N G.f. A(x) satisfies: [x^n] A_{2^(n-1)}(x) = 0 for n>2 where A_{n+1}(x) = A_{n}(A(x)) denotes iteration with A_0(x)=x.
%H Paul D. Hanna, <a href="/A177782/b177782.txt">Table of n, a(n), n = 1..50.</a>
%e G.f.: A(x) = x + 2*x^2 - 12*x^3 + 56*x^4 - 12080*x^5 +...
%e Coefficients in the (2^n)-th iterations of A(x), n=0..7, begin:
%e [1, 2, -12, 56, -12080, -9802944, -31002027840, ...];
%e [1, 4, -16, 0, -23296, -19776000, -62160338944, ...];
%e [1, 8, 0, -256, -47104, -40198144, -124955000832, ...];
%e [1, 16, 128, 0, -106496, -83165184, -252519120896, ...];
%e [1, 32, 768, 14336, 0, -175898624, -516100718592, ...];
%e [1, 64, 3584, 184320, 8454144, 0, -1064313028608, ...];
%e [1, 128, 15360, 1777664, 199622656, 21145583616, 0, ...];
%e [1, 256, 63488, 15482880, 3730571264, 888894652416, 205351244791808, 0, ...];
%e where the zeros along the diagonal illustrate the property
%e that the coefficient of x^n in A_{2^(n-1)} is zero for n>2.
%o (PARI) {a(n)=local(A=[1,2],G);for(m=3,n,A=concat(A,0);G=x*Ser(A); for(i=2,m,G=subst(G,x,G));A[ #A]=-polcoeff(G,#A)/(2^(#A-1)));A[n]}
%K sign
%O 1,2
%A _Paul D. Hanna_, May 17 2010
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