A210839 - OEIS

%I #18 May 10 2012 23:32:58

%S 1,1,1,3,7,17,45,121,333,937,2675,7735,22613,66711,198361,593873,

%T 1788697,5416097,16477471,50342595,154397465,475169249,1466983101,

%U 4542061223,14100318843,43879550851,136858661589,427747723605,1339505345521,4202281084715,13205593222009

%N G.f. satisfies: A(x) = x + A( x*A(x)/(1 - x*A(x)) ).

%C Compare the g.f. to the trivial identity:

%C G(x) = x + G( x*G(x)/(1 + x*G(x)) ) which holds when G(x) = x/(1-x).

%F G.f. satisfies: A(-A(-x)) = x.

%e G.f.: A(x) = x + x^2 + x^3 + 3*x^4 + 7*x^5 + 17*x^6 + 45*x^7 + 121*x^8 +...

%e Related expansion:

%e x*A(x)/(1-x*A(x)) = x^2 + x^3 + 2*x^4 + 5*x^5 + 11*x^6 + 28*x^7 + 73*x^8 + 195*x^9 + 536*x^10 + 1501*x^11 + 4269*x^12 + 12306*x^13 + 35869*x^14 +...

%o (PARI) {a(n)=local(A=x+x^2);for(i=1,n,A=x+subst(A,x,x*A/(1-x*A+x*O(x^n))));polcoeff(A,n)}

%o for(n=1,30,print1(a(n),", "))

%K nonn

%O 1,4

%A _Paul D. Hanna_, May 10 2012