A163136 G.f. A(x) equals an infinite symmetric composition of functions x+x^n, n=2,3,4,...

1, 2, 4, 13, 41, 133, 457, 1626, 5983, 22581, 86273, 332309, 1289466, 5037491, 19814253, 78464829, 312698663, 1253236364, 5047142834, 20408861265, 82804575274, 336913925731, 1374181645807, 5617148927835, 23007022273962

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Formula

G.f.: A(x) = ...o x+x^n o...o x+x^3 o x+x^2 o (x) o x+x^2 o x+x^3 o...o x+x^n o...

Example

G.f.: A(x) = x + 2*x^2 + 4*x^3 + 13*x^4 + 41*x^5 + 133*x^6 +...
G.f. A(x) equals the limit of symmetric compositions starting with:
(1) x+x^2 o x+x^2 = x + 2*x^2 + 2*x^3 + x^4 ;
(2) x+x^3 o x+x^2 o x+x^2 o x+x^3 = x + 2*x^2 + 4*x^3 + 11*x^4 +...;
(3) x+x^4 o x+x^3 o x+x^2 o x+x^2 o x+x^3 o x+x^4 = x + 2*x^2 + 4*x^3 + 13*x^4 +...

Prog

(PARI) {a(n)=local(F=x); if(n<1, 0, for(k=2, n, F=subst(subst(x+x^k, x, F), x, x+x^k +x*O(x^n)); ); return(polcoeff(F, n)))}

Crossrefs

Cf. A163137, A163134.

Sequence in context: A284193 A148255 A148256 * A325578 A118930 A355194

Adjacent sequences: A163133 A163134 A163135 * A163137 A163138 A163139

Keyword

nonn

Author

Paul D. Hanna, Aug 16 2009

Status

approved