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A096877
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Expansion in power series of a parametrization of the Folium of Descartes.
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1
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1, -2, -10, 0, -130, 256, 236, 0, -22730, 81920, 327668, 0, 777260, 0, -7180840, 0, -1051237338, 4362076160, 22662123300, 0, 227431418372, -549755813888, -1598030872600, 0, -7086115747780, -32435593019392, -311555637408376, 0
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OFFSET
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0,2
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COMMENTS
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Given g.f. A(x), then B(x) = x*A(x^3/4) satisfies 0 = f(B(x), B(x^2)) where f(u, v) = u^3 + v^3 - u*v.
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LINKS
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EXAMPLE
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G.f. = 1 - 2*x - 10*x^2 - 130*x^4 + 256*x^5 + 236*x^6 - 22730*x^8 + ...
B(x) = x - 1/2*x^4 - 5/8*x^7 - 65/128*x^13 + ...
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PROG
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(PARI) {a(n) = my(A, A2, m); if( n<0, 0, A = 1 + O(x); m = 1; while(m <= n, m *= 2; A = subst(A, x, 4*x^2); A2 = subst(A, x, 4*x^2); A = sqrt(4*x^2*A2^2 + A^3/A2) - 2*x*A2); polcoeff(A, 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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