A163136 - OEIS

%I #2 Mar 30 2012 18:37:17

%S 1,2,4,13,41,133,457,1626,5983,22581,86273,332309,1289466,5037491,

%T 19814253,78464829,312698663,1253236364,5047142834,20408861265,

%U 82804575274,336913925731,1374181645807,5617148927835,23007022273962

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

%F 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...

%e G.f.: A(x) = x + 2*x^2 + 4*x^3 + 13*x^4 + 41*x^5 + 133*x^6 +...

%e G.f. A(x) equals the limit of symmetric compositions starting with:

%e (1) x+x^2 o x+x^2 = x + 2*x^2 + 2*x^3 + x^4 ;

%e (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 +...;

%e (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 +...

%o (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)))}

%Y Cf. A163137, A163134.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Aug 16 2009