A145090 - OEIS

%I #2 Mar 30 2012 18:37:15

%S 1,1,3,9,34,131,542,2297,10043,44722,202669,930527,4321859,20264186,

%T 95802300,456152409,2185541010,10529301243,50976432986,247881491762,

%U 1210135732693,5928928117319,29142693939368,143671971795711

%N G.f. satisfies: A(x) = A(y^2)/(1-y) where y = x*A(x).

%F G.f. satisfies: A(x) = (1-z)*A( z*(1-z)/A(x) ) where z = sqrt(x).

%e A(x) = 1 + x + 3*x^2 + 9*x^3 + 34*x^4 + 131*x^5 + 542*x^6 + 2297*x^7 +...

%e A(x*(1-x)/A(x^2))*(1-x) = 1 + x^2 + 3*x^4 + 9*x^6 + 34*x^8 + 131*x^10 +...

%o (PARI) {a(n)=local(A=1+x);for(n=1,n,A=1/x*serreverse(x/(subst(A,x,x^2+x*O(x^33))/(1-x))));polcoeff(A,n)}

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 21 2008