A196866 G.f. A(x) satisfies: A(x)^4 + A(-x)^4 = 2 and A(x)^-4 - A(-x)^-4 = -32*x.

1, 4, -24, -800, 9824, 381824, -5715712, -236348416, 3885237760, 166141515776, -2884493168640, -125973507063808, 2266868356071424, 100441740460359680, -1853741093854511104, -83006642599731134464, 1561071322451916750848, 70464426394180291919872

Offset

0,2

Links

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

Formula

G.f.: ( 2*(sqrt(1+4*4^4*x^2) + 2*4^2*x)/(sqrt(1+4*4^4*x^2) + 1) )^(1/8).

Example

 G.f.: A(x) = 1 + 4*x - 24*x^2 - 800*x^3 + 9824*x^4 + 381824*x^5 +...
where
A(x)^4 = 1 + 16*x - 4096*x^3 + 2097152*x^5 - 1342177280*x^7 +...
A(x)^-4 = 1 - 16*x + 256*x^2 - 65536*x^4 + 33554432*x^6 - 21474836480*x^8 +...

Prog

 (PARI) {a(n)=local(A=[1, 4]); for(k=2, n, A=concat(A, 0); if(k%2==0, 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((2*(sqrt(1+4*4^4*X^2) + 2*4^2*x)/(sqrt(1+4*4^4*X^2) + 1) )^(1/8), n)}

Crossrefs

Cf. A196867, A193618, A193619, A196864, A196865, A196868, A196869.

Sequence in context: A012989 A347480 A058171 * A326794 A223005 A009043

Adjacent sequences: A196863 A196864 A196865 * A196867 A196868 A196869

Keyword

sign

Author

Paul D. Hanna, Oct 06 2011

Status

approved