A143562 - OEIS

%I #6 Jun 04 2012 12:53:00

%S 1,1,5,17,105,481,3261,16801,119697,656129,4819061,27447601,205776121,

%T 1202943457,9152680109,54524185409,419491297313,2534963932417,

%U 19673179986661,120224135048273,939543098579081,5793676726569697

%N G.f. satisfies: A(x) = 1 + x*A(x)^3/A(-x)^2.

%F G.f. satisfies: A(x) + A(-x) = 1 + (1+x^2)*A(x)*A(-x).

%F G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(2*n) / A(-x)^(2*n).

%F G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x)^(2*n)/A(-x)^(2*n) * x^n/n ).

%F G.f.: A(x) = G(x)/(1+x^2) where G(x) = 1 + x*G(x)^3/G(-x)^3 is the g.f. of A143556.

%e G.f. A(x) = 1 + x + 5*x^2 + 17*x^3 + 105*x^4 + 481*x^5 + 3261*x^6 +...

%e A(x)*A(-x) = 1 + 9*x^2 + 201*x^4 + 6321*x^6 + 233073*x^8 +...

%o (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^3/subst(A^2,x,-x));polcoeff(A,n)}

%Y Cf. A143556, A143339.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 24 2008