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%I #5 Jul 20 2023 15:59:56
%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).
%F D-finite with recurrence 5*n*(n-1)*(6947*n-150973)*a(n) +(n-1)*(909994*n^2 -5636597*n +10466184)*a(n-1) +(-3594151*n^3 +36668949*n^2 -116071772*n +115774518)*a(n-2) +(3752530*n^3 -43272273*n^2 +163807289*n -203448234)*a(n-3) +(-5236321*n^3 +69827238*n^2 -307215935*n +448390974)*a(n-4) +4*(1072898*n^3 -16156263*n^2 +76788526*n -112806741)*a(n-5) -48*(n-7) *(36817*n^2 -393746*n +906725)*a(n-6) -256*(12938*n-42081) *(n-7)*(n-8) *a(n-7)=0. - _R. J. Mathar_, Jul 20 2023
%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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