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

1, 2, 12, 364, 49280, 27297360, 59855127360, 515600292989376, 17478262497392546432, 2341170788069821884925696, 1243964516830446590036473921536, 2629751195406987463208250109864126464

Offset

1,2

Links

Paul D. Hanna, Table of n, a(n), n = 1..40.

Example

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,(515600292989376),...;
1,256,65280,16613760,4222658560,1072200161920,272033712041216,68973668731925376,(17478262497392546432),...;
...
where the terms in parenthesis form the initial terms of this sequence.

Prog

(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))}

Crossrefs

Cf. A158260, A158262, A158263, A158264 (table).

Sequence in context: A006939 A152686 A131690 * A215956 A251182 A266241

Adjacent sequences: A158258 A158259 A158260 * A158262 A158263 A158264

Keyword

nonn

Author

Paul D. Hanna, Mar 15 2009

Status

approved