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%I #2 Mar 30 2012 18:37:16
%S 1,8,240,30256,15665664,32668147008,272033712041216,
%T 9024264001164470016,1192791193150627685091840,
%U 628748300357129103400036998144,1322980853407936018020929177243811840
%N a(n) = coefficient of x^n in the (2^(n+1))-th iteration of x+x^2 for n>=1.
%e Table of coefficients in the (2^i)-th iteration of x+x^2 begins:
%e 1,1;
%e 1,2,2,1;
%e (1),4,12,30,64,118,188,258,302,298,244,162,84,32,8,1;
%e 1,(8),56,364,2240,13188,74760,409836,2179556,11271436,56788112,...;
%e 1,16,(240),3480,49280,685160,9383248,126855288,1695695976,...;
%e 1,32,992,(30256),912640,27297360,810903456,23950328688,...;
%e 1,64,4032,252000,(15665664),969917088,59855127360,3683654668512,...;
%e 1,128,16256,2056384,259445760,(32668147008),4106848523904,...;
%e 1,256,65280,16613760,4222658560,1072200161920,(272033712041216),...;
%e 1,512,261632,133563136,68139438080,34745409189120,17710292513905152,(9024264001164470016),...;
%e ...
%e Where the terms in parenthesis form the initial terms of this sequence.
%o (PARI) {a(n)=local(G=x+x^2+x*O(x^n)); if(n<0, 0, for(i=1, n+1, G=subst(G, x, G+x*O(x^n))); polcoeff(G, n, x))}
%Y Cf. A158260, A158261, A158262, A158264 (table).
%K nonn
%O 1,2
%A _Paul D. Hanna_, Mar 15 2009
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