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A196866
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G.f. A(x) satisfies: A(x)^4 + A(-x)^4 = 2 and A(x)^-4 - A(-x)^-4 = -32*x.
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5
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1, 4, -24, -800, 9824, 381824, -5715712, -236348416, 3885237760, 166141515776, -2884493168640, -125973507063808, 2266868356071424, 100441740460359680, -1853741093854511104, -83006642599731134464, 1561071322451916750848, 70464426394180291919872
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: ( 2*(sqrt(1+4*4^4*x^2) + 2*4^2*x)/(sqrt(1+4*4^4*x^2) + 1) )^(1/8).
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EXAMPLE
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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 +...
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PROG
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(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)}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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