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例子
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x+x^2第(2^n)次迭代的系数表开始于:
1,1,0,0,0,0,0,0,0,0,0,0,0,0,...;
1,2,2,1,0,0,0,0,0,0,0,0,0,0,...;
1,4,12,30,64118188258302298244162,84,32,8,1,0,0,0,0,。。。;
1,8,56,364,2240,13188,74760,409836,2179556,11271436,56788112,...;
1,16,240,3480,49280,685160,9383248,126855288,1695695976,...;
1,32,992,30256,912640,27297360,810903456,23950328688,...;
1,64,4032,252000,15665664,969917088,59855127360,3683654668512,...;
1,128,16256,2056384,259445760,32668147008,4106848523904,...;
1,256,65280,16613760,4222658560,1072200161920,272033712041216,...;
1,512,261632,133563136,68139438080,34745409189120,17710292513905152,...;
...
初始列g.f.s如下:
k=1:1/(1-2x);
k=2:2x/((1-2x)(1-4x));
k=3:(x+16x^2)/((1-2x)(1-4x)(1~8x));
k=4:(64x^2+320x^3)/(1-2x)(1-4x)(1-16x));
k=5:(118x^2+5872x^3+13824x^4)/(1-2x)(1-4x)(1-16x)(1-3));
...
g.f.s列分子中的系数形成三角形:
1;
0,2;
0,1,16;
0,0,64320;
0,0,118,5872,13824;
0,0,188,51072,942592,1179648;
0,0,258,344304,28261632,278323200,179306496;
0,0,302,2025536,610203136,25398255616,152690491392,37044092928; ...
其中主对角线开始:
[1,2,16,320,13824,1179648,179306496,37044092928,-9947144257536,...];
三角形的行和开始于:
[1,2,17,384,19814,2173500,486235890,215745068910,186016597075722,...].
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