A096877 - OEIS

%I #4 Aug 21 2019 13:01:41

%S 1,-2,-10,0,-130,256,236,0,-22730,81920,327668,0,777260,0,-7180840,0,

%T -1051237338,4362076160,22662123300,0,227431418372,-549755813888,

%U -1598030872600,0,-7086115747780,-32435593019392,-311555637408376,0

%N Expansion in power series of a parametrization of the Folium of Descartes.

%C 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.

%e G.f. = 1 - 2*x - 10*x^2 - 130*x^4 + 256*x^5 + 236*x^6 - 22730*x^8 + ...

%e B(x) = x - 1/2*x^4 - 5/8*x^7 - 65/128*x^13 + ...

%o (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))};

%K sign

%O 0,2

%A _Michael Somos_, Jul 14 2004