A143562 G.f. satisfies: A(x) = 1 + x*A(x)^3/A(-x)^2.

1, 1, 5, 17, 105, 481, 3261, 16801, 119697, 656129, 4819061, 27447601, 205776121, 1202943457, 9152680109, 54524185409, 419491297313, 2534963932417, 19673179986661, 120224135048273, 939543098579081, 5793676726569697

Offset: 0

Author

Paul D. Hanna, Aug 24 2008

Keywords

• nonn

Examples

			G.f. A(x) = 1 + x + 5*x^2 + 17*x^3 + 105*x^4 + 481*x^5 + 3261*x^6 +...
A(x)*A(-x) = 1 + 9*x^2 + 201*x^4 + 6321*x^6 + 233073*x^8 +...
		

Crossrefs

Cf. A143556, A143339.

Programs

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)}

Formula

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

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

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

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.