|
%I #5 Mar 30 2012 18:37:31
%S 1,4,-24,-800,9824,381824,-5715712,-236348416,3885237760,166141515776,
%T -2884493168640,-125973507063808,2266868356071424,100441740460359680,
%U -1853741093854511104,-83006642599731134464,1561071322451916750848,70464426394180291919872
%N G.f. A(x) satisfies: A(x)^4 + A(-x)^4 = 2 and A(x)^-4 - A(-x)^-4 = -32*x.
%F G.f.: ( 2*(sqrt(1+4*4^4*x^2) + 2*4^2*x)/(sqrt(1+4*4^4*x^2) + 1) )^(1/8).
%e G.f.: A(x) = 1 + 4*x - 24*x^2 - 800*x^3 + 9824*x^4 + 381824*x^5 +...
%e where
%e A(x)^4 = 1 + 16*x - 4096*x^3 + 2097152*x^5 - 1342177280*x^7 +...
%e A(x)^-4 = 1 - 16*x + 256*x^2 - 65536*x^4 + 33554432*x^6 - 21474836480*x^8 +...
%o (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]}
%o (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)}
%Y Cf. A196867, A193618, A193619, A196864, A196865, A196868, A196869.
%K sign
%O 0,2
%A _Paul D. Hanna_, Oct 06 2011
|
