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A112482 Expansion of the solution of a functional equation. 1

%I

%S 1,1,1,2,4,8,17,38,87,203,482,1160,2822,6930,17157,42775,107300,

%T 270623,685842,1745651,4460450,11437423,29421695,75906148,196358971,

%U 509209381,1323524122,3447340550,8996802898,23522607256,61606041763,161604774963

%N Expansion of the solution of a functional equation.

%F Series reversion of g.f. A(x) is -A(-x).

%F Given g.f. A(x) and B(x) = g.f. of A089796, then B(x)=x+A(x*B(x)).

%F G.f. A(x)=y satisfies 0=y^3+(-x-1)*y^2+(x^2+3*x-1)*y+(-x^3-x^2+x).

%o (PARI) {a(n)=local(A); if(n<1, 0, A=O(x); for(k=1,n, A=A^3+(-x-1)*A^2+(x^2+3*x)*A+(-x^3-x^2+x)); polcoeff(A,n))}

%K nonn

%O 1,4

%A _Michael Somos_, Sep 08 2005

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Last modified June 20 09:27 EDT 2021. Contains 345162 sequences. (Running on oeis4.)