A143557 G.f. satisfies: A(x) = 1 + x*A(x)^4/A(-x)^4.

1, 1, 8, 32, 280, 1728, 16744, 117856, 1202552, 9044352, 95203784, 745451168, 8011827928, 64459117632, 703166465320, 5769038826208, 63639465830712, 529889242505984, 5896324892061576, 49665617425122592, 556508207889107096

Offset: 0

Author

Paul D. Hanna, Aug 24 2008

Keywords

• nonn

Examples

			G.f. A(x) = 1 + x + 8*x^2 + 32*x^3 + 280*x^4 + 1728*x^5 + 16744*x^6 +...
A(x)/A(-x) = 1 + 2*x + 2*x^2 + 50*x^3 + 98*x^4 + 2658*x^5 + 6370*x^6 +...
A(x)^3/A(-x)^3 = 1 + 6*x + 18*x^2 + 182*x^3 + 930*x^4 + 10374*x^5 +...
where 1 - (1+x^2)/A(x) = x*A(x)^3/A(-x)^3.
		

Crossrefs

Cf. A143564, A143555, A143556, A143558, A143559.

Programs

PARI

{a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^4/subst(A^4,x,-x));polcoeff(A,n)}

Formula

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

G.f. satisfies: A(x) = 1 + x^2 + x*A(x)^4 / A(-x)^3.

G.f. satisfies: (A(x) - 1)^3 = ( 1 - (1+x^2)/A(x) )^4/x = x^3*A(x)^12/A(-x)^12.

G.f.: A(x) = (1+x^2)*G(x) where G(x) = 1 + x*G(x)^4/G(-x)^3 is the g.f. of A143564.