OFFSET
0,3
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.
EXAMPLE
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.
PROG
(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)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 24 2008
STATUS
approved