三角形T开始于:
1;
1,1;
5,2,1;
70,16,3,1;
1973,308,33,4,1;
94216,11048,810,56,5,1;
6851197,639972,35325,1672,85,6,1;
706335064,54671188,2408568,85904,2990,120,7,1;
98105431657,6471586298,236624733,6741544,176885,4860,161,8,1;
17669939141440,1014487323984,31654735416,749040472,15706200,325368,7378,208,9,1;
...
形成x*exp(x)迭代中的系数表,如下所示:
n=0:[1,0,0,0,0,…];
n=1:[1,1,1/2!,1/3!,1/4!,1/5!,1/6!,…];
n=2:[1,2,6/2!,23/3!,104/4!,537/5!,3100/6!,…];
n=3:[1,3,15/2!,102/3!,861/4!,8598/5!,98547/6!,…];
n=4:[1,4,28/2!,274/3!,3400/4!,50734/5!,880312/6!,…];
n=5:[1,5,45/2!,575/3!,9425/4!,187455/5!,4367245/6!,…];
n=6:[1,6,66/2!,1041/3!,21216/4!,527631/5!+15441636/6!,…];
n=7:[1,7,91/2!,1708/3!,41629/4!,1242892/5!,43806175/6!,…];
n=8:[1,8120/2!,2612/3!,74096/4!,2582028/5!,106459312/6!,…];
...
并根据该三角形T构造矩阵D:D(n,k)=T(n,k)/(n-k)!,
然后矩阵D变换上表中的对角线,如下所示:
对角线开始的位置:
A174481号: [1, 1, 6/2!, 102/3!, 3400/4!, 187455/5!, ...];
A174482号: [1, 2, 15/2!, 274/3!, 9425/4!, 527631/5!, ...];
174483英镑: [1, 3, 28/2!, 575/3!, 21216/4!, 1242892/5!, ...];
A174484号: [1, 4, 45/2!, 1041/3!, 41629/4!, 2582028/5!, ...].