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A158262 a(n) = coefficient of x^n in the (2^n)-th iteration of x+x^2 for n>=1.

%I A158262 #2 Mar 30 2012 18:37:16
%S A158262 1,4,56,3480,912640,969917088,4106848523904,68973668731925376,
%T A158262 4597014244761562326272,1218175506582318206655794688,
%U A158262 1285897546575275148015361075150848
%N A158262 a(n) = coefficient of x^n in the (2^n)-th iteration of x+x^2 for n>=1.
%e A158262 Table of coefficients in the (2^i)-th iteration of x+x^2 begins:
%e A158262 1,1;
%e A158262 (1),2,2,1;
%e A158262 1,(4),12,30,64,118,188,258,302,298,244,162,84,32,8,1;
%e A158262 1,8,(56),364,2240,13188,74760,409836,2179556,11271436,56788112,...;
%e A158262 1,16,240,(3480),49280,685160,9383248,126855288,1695695976,...;
%e A158262 1,32,992,30256,(912640),27297360,810903456,23950328688,...;
%e A158262 1,64,4032,252000,15665664,(969917088),59855127360,3683654668512,...;
%e A158262 1,128,16256,2056384,259445760,32668147008,(4106848523904),...;
%e A158262 1,256,65280,16613760,4222658560,1072200161920,272033712041216,(68973668731925376),...;
%e A158262 ...
%e A158262 Where the terms in parenthesis form the initial terms of this sequence.
%o A158262 (PARI) {a(n)=local(G=x+x^2+x*O(x^n)); if(n<0, 0, for(i=1, n, G=subst(G, x, G+x*O(x^n))); polcoeff(G, n, x))}
%Y A158262 Cf. A158260, A158261, A158263, A158264 (table).
%K A158262 nonn
%O A158262 1,2
%A A158262 _Paul D. Hanna_, Mar 15 2009