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A158261 a(n) = coefficient of x^n in the (2^(n-1))-th iteration of x+x^2 for n>=1.

%I A158261 #4 Mar 30 2012 18:37:16
%S A158261 1,2,12,364,49280,27297360,59855127360,515600292989376,
%T A158261 17478262497392546432,2341170788069821884925696,
%U A158261 1243964516830446590036473921536,2629751195406987463208250109864126464
%N A158261 a(n) = coefficient of x^n in the (2^(n-1))-th iteration of x+x^2 for n>=1.
%H A158261 Paul D. Hanna, <a href="/A158261/b158261.txt">Table of n, a(n), n = 1..40.</a>
%e A158261 Table of coefficients in the (2^i)-th iteration of x+x^2 begins:
%e A158261 (1),1;
%e A158261 1,(2),2,1;
%e A158261 1,4,(12),30,64,118,188,258,302,298,244,162,84,32,8,1;
%e A158261 1,8,56,(364),2240,13188,74760,409836,2179556,11271436,56788112,...;
%e A158261 1,16,240,3480,(49280),685160,9383248,126855288,1695695976,...;
%e A158261 1,32,992,30256,912640,(27297360),810903456,23950328688,...;
%e A158261 1,64,4032,252000,15665664,969917088,(59855127360),3683654668512,...;
%e A158261 1,128,16256,2056384,259445760,32668147008,4106848523904,(515600292989376),...;
%e A158261 1,256,65280,16613760,4222658560,1072200161920,272033712041216,68973668731925376,(17478262497392546432),...;
%e A158261 ...
%e A158261 where the terms in parenthesis form the initial terms of this sequence.
%o A158261 (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 A158261 Cf. A158260, A158262, A158263, A158264 (table).
%K A158261 nonn
%O A158261 1,2
%A A158261 _Paul D. Hanna_, Mar 15 2009