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例子
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G.f.:A(x,y,z)=1/(1-x-x*y)
+2*(7+4*z+z^2)*x^2*y/(1-x-x*y)^5
+6*(131+176*z+96*z^2+16*z^3+z^4)*x^4*y^2/(1-x-x*y)^9
+20*(3067+6588*z+5895*z^2+2416*z^3+477*z^4+36*z^5+z^6)*x^6*y^3/(1-x-x*y)^13+。。。
z=x+xy时的G.f.产生:A(x,y,x+xy)=1+(1+y)*x
+(1+16*y+y^2)*x^2
+(1+81*y+81*y^2+y^3)*x^3
+(1+256*y+1296*y^2+256*y ^3+y ^4)*x ^4
+(1+625*y+10000*y^2+10000*y^3+625*y^4+y^5)*x^5+。。。
这是一个包含二项式系数到四次方的级数。
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z^k的系数T(n,k)三角形,k=0..2n,开始于:
[1];
[7, 4, 1];
[131, 176, 96, 16, 1];
[3067, 6588, 5895, 2416, 477, 36, 1];
[79459, 235456, 298816, 197824, 73120, 14656, 1504, 64, 1];
[2181257, 8252300, 13668975, 12563200, 6966400, 2373504, 490700, 58400, 3675, 100, 1];
[62165039, 286326288, 587324232, 692965040, 516541455, 252283968, 81432456, 17138304, 2276145, 179440, 7632, 144, 1];
[1818812387, 9876304172, 24205612067, 34939683632, 32837525567, 21029302364, 9356637759, 2899564224, 619135629, 88879924, 8237341, 461776, 14161, 196, 1];
[54257991011, 339398092544, 968547444480, 1655445817088, 1881608595776, 1496188189440, 853911382016, 353544477440, 106191762336, 22927328512, 3492995968, 364541184, 24932320, 1044736, 24192, 256, 1];
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