高校数学の質問スレ（医者・東大卒専用） Part438

f[n_,x_] = f[n]=If[
n==1,
1/(1-x),
1/(1-(1-(2^n-2)/3^(n-1))x) x Sum[Binomial[n,m]/3^(n-1)f[m,x],{m,1,n-1}]]
Table[{n,SeriesCoefficient[f[11,x],{x,0,n}]},{n,9,15}]
Table[{n,SeriesCoefficient[f[11,x]*(1-x),{x,0,n}]},{n,9,5}]
Table[{n,N@SeriesCoefficient[f[11,x]*(1-x),{x,0,n}]},{n,0,20}]
Table[{n,Sign@SeriesCoefficient[f[11,x]*(1-2*x+x^2),{x,0,n}]},{n,0,20}]
ListPlot[Table[SeriesCoefficient[f[11,x]*(1-x),{x,0,n}],{n,30}]]
N@SeriesCoefficient[1/(1-x)-f[11,x],{x,1,0}]