A145072 - OEIS

%I #2 Mar 30 2012 18:37:14

%S 1,1,2,5,15,48,163,573,2074,7669,28860,110148,425384,1659185,6526791,

%T 25863949,103151955,413728474,1667757766,6753022725,27454555171,

%U 112024545382,458616153319,1883201461892,7754348091640,32010908796160

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

%F G.f. satisfies: A(x) = A( [z/(1+z)]/A(x) )/(1+z) where z = sqrt(x).

%e A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 48*x^5 + 163*x^6 + 573*x^7 +...

%e A([x/(1+x)]/A(x^2))/(1+x) = 1 + x^2 + 2*x^4 + 5*x^6 + 15*x^8 + 48*x^10 +...

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 21 2008