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A158260 a(n) = coefficient of x^n in the [2^(n-2)]-th iteration of x+x^2 for n>=2.

%I A158260 #2 Mar 30 2012 18:37:16
%S A158260 1,2,30,2240,685160,810903456,3683654668512,64657586863790400,
%T A158260 4426882384548801561472,1192052411353154132337483776,
%U A158260 1270174918862853255008627489608704
%N A158260 a(n) = coefficient of x^n in the [2^(n-2)]-th iteration of x+x^2 for n>=2.
%e A158260 Table of coefficients in the (2^i)-th iteration of x+x^2 begins:
%e A158260 1,(1);
%e A158260 1,2,(2),1;
%e A158260 1,4,12,(30),64,118,188,258,302,298,244,162,84,32,8,1;
%e A158260 1,8,56,364,(2240),13188,74760,409836,2179556,11271436,56788112,...;
%e A158260 1,16,240,3480,49280,(685160),9383248,126855288,1695695976,...;
%e A158260 1,32,992,30256,912640,27297360,(810903456),23950328688,...;
%e A158260 1,64,4032,252000,15665664,969917088,59855127360,(3683654668512),...;
%e A158260 1,128,16256,2056384,259445760,32668147008,4106848523904,515600292989376,(64657586863790400),...;
%e A158260 ...
%e A158260 where the terms in parenthesis form the initial terms of this sequence.
%o A158260 (PARI) {a(n)=local(G=x+x^2+x*O(x^n)); if(n<2, 0, for(i=1, n-2, G=subst(G, x, G)); polcoeff(G, n, x))}
%Y A158260 Cf. A158261, A158262, A158263, A158264 (table).
%K A158260 nonn
%O A158260 2,2
%A A158260 _Paul D. Hanna_, Mar 15 2009