■いろいろの漸化式と母関数(その5)

[1]f(x)=(x^2n+x^2n-1)/(x−1)^2n

 f(1/x)=x^-(2n-1)f(x)

C=1,D=2n−1

[2]f(x)=Σ(n,k)^2x^n+k/(x−1)^2n

 f(1/x)=x^-nf(x)

C=1,D=n

[3]f(x)=Σ1/2n・(2n,k)(2n+1,k)^2x^2n+1+k/(x−1)^4n

 f(1/x)=x^-nf(x)

C=1,D=2n−1

[4]f(x)=(x^16+10x^15+28x^14+28x^13+10x12+x^11)/(x−1)^16

 f(1/x)=x^-11f(x)

C=1,D=11

[5]f(x)=x^m/(x−1)^r

 f(1/x)=(−1)^rx^-(2m-r)f(x)

C=(−1)^r,D=2m−r

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