例如:A(x)=1+x+3*x^2/2!+21*x^3/3!+241*x^4/4!+3951*x^5/5! +...
为了说明术语是如何生成的,请形成系数表x^k/k!,k>=0,in(积分A(x)^n dx)^ n表示n>=0如下:
n=0:[1,0,0,0,0,0,0,0,0,0,0,…];
n=1:[0,1,1,3,21,241,3951,85499,2325205,76860673,…];
n=2:[0,0,2,12,88,920,13328,254744,6161568,182632584,…];
n=3:[0,0,0,6,108,1710,29700,600642,14344092,403670790,…];
n=4:[0,0,0,0,24,960,28800,826560,24665088,793449216,…];
n=5:[0,0,0,0,0,120,9000,462000,20958000,922005000,…];
n=6:[0,0,0,0,720,90720,7378560,504040320,…];
n=7:[0,0,0,0,0,0,1,0,5040,987840,120022560,…];
n=8:[0,0,0,0,0,0,10,04032011612160,…];
n=9:[0,0,0,0,0,0,1,0,362880,…]; ...
然后,列和构成这个序列的项。