>>48,65,81
　1 -cos(x) = (1/2!)x^2 -(1/4!)x^4 +(1/6!)x^6 -(1/8!)x^8 +(1/10!)x^10 -(1/12!)x^12 +(1/14!)x^14 + ･･･.
　f(x) = sin(x/2)/sin(3x/2) = 1/{3-4sin(x/2)^2} = 1/{3-2[1-cos(x)]}
　= (1/3) +(2/9)(1/2!)x^2 +(2/3)(1/4!)x^4 +(14/3)(1/6!)x^6 + (1618/27)(1/8!)x^8 +(3694/3)(1/10!)x^10 +(111202/3)(1/12!)x^12 +(13842922/9)(1/14!)}x^14 +･･･

　f(0)=1/3,　f^(2)(0)=2/9,　f^(4)(0)=2/3,　f^(6)(0)=14/3,　f^(8)(0)=1618/27,　f^(10)(0)=3694/3,　f^(12)(0)=111202/3,　f^(14)(0)=13842922/9,
　f^(2k+1)(0) =0.

　∴ j+k が奇数の要素は M[j,k] = f^(j+k-2)(x) =0.
　∴ A(n) = Ao(n)･Ae(n).
　ここに、Ao(n)はM(n)の奇数行・奇数列からなる小行列式、Ae(n)はM(n)の偶数行･偶数列からなる小行列式。

(例)
　Ao(1)=Ao(2)=1/3, Ao(3)=Ao(4)=14/(3^4), Ao(5)=Ao(6)=9152/(3^7).
　Ae(1)=1, Ae(2)=Ae(3)=2/9, Ae(4)=Ae(5)=16/(3^3), Ae(6)=Ae(7)=1331200/(3^8).

　A(1)=1/3, A(2)=2/27, A(3)=28/(3^6), A(4)=224/(3^7), A(5)=146432/(3^10), A(6)=1218314240/(3^15), ･･･