A143561 - OEIS

%I #2 Mar 30 2012 18:37:11

%S 1,2,9,24,88,280,1064,3672,14456,52184,210504,782232,3210904,12176792,

%T 50638440,194956248,818961080,3189915224,13508052104,53105011480,

%U 226355549400,896636646936,3842662060200,15317408281944,65946510374136

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

%F G.f. satisfies: (1+x^2)^2 - 2*(1+x^2)*G(x) + (1+x)*G(x)^2 - x*G(x)^3 = 0 where G(x)^2 = A(x) and G(x) = 1 + x*A(x)/A(-x) is the g.f. of A143555.

%e G.f.: A(x) = 1 + 2*x + 9*x^2 + 24*x^3 + 88*x^4 + 280*x^5 + 1064*x^6 +...

%e A(x)/A(-x) = 1 + 4*x + 8*x^2 + 28*x^3 + 80*x^4 + 308*x^5 + 984*x^6 +...

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

%Y Cf. A143555.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 24 2008