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

Author

Paul D. Hanna, Oct 06 2011

Keywords

• sign

Examples

			 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 +...
		

Crossrefs

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

Programs

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)}

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).