A158263 a(n) = coefficient of x^n in the (2^(n+1))-th iteration of x+x^2 for n>=1.

1, 8, 240, 30256, 15665664, 32668147008, 272033712041216, 9024264001164470016, 1192791193150627685091840, 628748300357129103400036998144, 1322980853407936018020929177243811840

Offset: 1

Author

Paul D. Hanna, Mar 15 2009

Keywords

• nonn

Examples

			Table of coefficients in the (2^i)-th iteration of x+x^2 begins:
1,1;
1,2,2,1;
(1),4,12,30,64,118,188,258,302,298,244,162,84,32,8,1;
1,(8),56,364,2240,13188,74760,409836,2179556,11271436,56788112,...;
1,16,(240),3480,49280,685160,9383248,126855288,1695695976,...;
1,32,992,(30256),912640,27297360,810903456,23950328688,...;
1,64,4032,252000,(15665664),969917088,59855127360,3683654668512,...;
1,128,16256,2056384,259445760,(32668147008),4106848523904,...;
1,256,65280,16613760,4222658560,1072200161920,(272033712041216),...;
1,512,261632,133563136,68139438080,34745409189120,17710292513905152,(9024264001164470016),...;
...
Where the terms in parenthesis form the initial terms of this sequence.
		

Crossrefs

Cf. A158260, A158261, A158262, A158264 (table).

Programs

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))}