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例子
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例如:A(x)=1+x+4*x^2!+31*x^3/3!+368*x^4/4!+5941*x^5/5!+。。。
相关扩展。
A(x)^2=1+2*x+10*x^2/2!+86*x^3/3!+1080*x^4/4!+18042*x^5/5!+。。。
1/(1+sinh(x))^2=1-2*x+6*x^2/2!-26*x^3/3!+144*x^4/4!-962*x^5/5!+。。。
(1+sinh(x))的奇次幂中[x^n/n!]的系数开始:
1:[(1),1,0,1,0,1,0,1,0,1,0,1,1,0,…];
3: [1,(3), 6, 9, 24, 63, 96, 549, 384, 4923, 1536, 44289,...];
5: [1, 5,(20), 65, 200, 725, 2720, 9665, 41600, 165125,...];
7: [1, 7, 42,(217), 1008, 4627, 22512, 112357, 567168,...];
9: [1, 9, 72, 513,(3312), 20169, 122112, 756513, 4770432,...];
11:[1, 11, 110, 1001, 8360,(65351), 492800, 3693701, 27948800,...];
13:[1, 13, 156, 1729, 17784, 171613,(1581216), 14210209,...];
15:[1, 15, 210, 2745, 33600, 387675, 4262160,(45293445),...];
17:[1, 17, 272, 4097, 58208, 783377, 10057472, 124378817,(1498389248), ...]; ...
其中括号中的系数生成如下序列:
[1, 3/3, 20/5, 217/7, 3312/9, 65351/11, 1581216/13, 45293445/15,...].
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