A196867 G.f. A(x) satisfies: A(x)^-4 + A(-x)^-4 = 2 and A(x)^4 - A(-x)^4 = 32*x.

1, 4, 40, -544, -14240, 240512, 7905536, -144081920, -5248825856, 99459618816, 3842132979712, -74547398033408, -2991092285194240, 58965437254402048, 2429529032173420544, -48445417122664284160, -2035619492638819483648, 40941665274780773253120

Offset

0,2

Links

Table of n, a(n) for n=0..17.

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

Cf. A196866, A193618, A193619, A196864, A196865, A196868, A196869.

Sequence in context: A092812 A349516 A290575 * A276362 A302178 A272261

Adjacent sequences: A196864 A196865 A196866 * A196868 A196869 A196870

Keyword

sign

Author

Paul D. Hanna, Oct 06 2011

Status

approved