OFFSET
0,2
FORMULA
G.f.: ( (sqrt(1+4*4^4*x^2) + 2*4^2*x)*(sqrt(1+4*4^4*x^2) + 1)/2 )^(1/8).
EXAMPLE
G.f.: A(x) = 1 + 4*x + 40*x^2 - 544*x^3 - 14240*x^4 + 240512*x^5 +...
where
A(x)^4 = 1 + 16*x + 256*x^2 - 65536*x^4 + 33554432*x^6 +...
A(x)^-4 = 1 - 16*x + 4096*x^3 - 2097152*x^5 + 1342177280*x^7 +...
PROG
(PARI) {a(n)=local(A=[1, 4]); for(k=2, n, A=concat(A, 0); if(k%2==1, A[#A]=-Vec(Ser(A)^4)[#A]/4, A[#A]=Vec(Ser(A)^-4)[#A]/4)); A[n+1]}
(PARI) {a(n)=local(X=x+x*O(x^n)); polcoeff(((sqrt(1+4*4^4*X^2) + 2*4^2*x)*(sqrt(1+4*4^4*X^2) + 1)/2 )^(1/8), n)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Oct 06 2011
STATUS
approved