E(t)=(1+t+t^2/2!+......+..)^2*(1+t^2/2!+t^4/4!+..+)^2
    =e^2t*((e^t+e^-t)/2)^2
    =1/4(e^4t+2*e^2t)
    =sigma(1/4*[4^n+2*2^n]*t^n/n!) n=0,1,2,，，


  ==> a(n)=1/4(4^n+2*2^n)

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