1,2

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,(68973668731925376),...;

...

Where the terms in parenthesis form the initial terms of this sequence.

(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))}

Cf. A158260, A158261, A158263, A158264 (table).

Sequence in context: A091797 A007726 A113113 this_sequence A089035 A089516 A000573

Adjacent sequences: A158259 A158260 A158261 this_sequence A158263 A158264 A158265

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Mar 15 2009