三角形开始:
1;
1, 0;
3, 1, 0;
11, 5, 1, 0;
56, 32, 7, 1, 0;
324, 204, 57, 9, 1, 0;
2324, 1604, 487, 89, 11, 1, 0;
18332, 13292, 4441, 897, 128, 13, 1, 0;
167544, 127224, 44712, 9864, 1486, 174, 15, 1, 0;
1674264, 1311384, 485592, 111744, 18486, 2286, 227, 17, 1, 0;
18615432, 14986632, 5735616, 1393872, 240318, 31734, 3329, 287, 19, 1, 0;
223686792, 183769992, 72550296, 18223632, 3296958, 455742, 51009, 4647, 354, 21, 1, 0;
2937715296, 2458713696, 993598248, 257587416, 48076704, 6958656, 801880, 77896, 6272, 428, 23, 1, 0;
41233157952, 35006137152, 14438206776, 3835359192, 738870048, 110022696, 13300084, 1330300, 114164, 8236, 509, 25, 1, 0; ...
生成功能。
通用公式:A(x,y)=1+(1)*x+(3+y)*x^2/2!+(11+5*y+y^2)*x^3/3+
(56+32*y+7*y^2+y^3)*x^4/4+
(324+204*y+57*y ^2+9*y ^3+y ^4)*x ^5/5+
(2324+1604*y+487*y^2+89*y^3+11*y^4+y^5)*x^6/6!+。。。
这样的话
A(x,y)=经验(y)*P(x)-Q(x,y)
哪里
P(x)=1/产品{n>=1}(1-x^n/n)=和{n>=0}A007841号(n) *x^n/n!,和
Q(x,y)=和{n>=1}y^n/产品{k=1..n}(k-x^k)。
更明确地说,
P(x)=1/((1-x)*(1-x^2/2)*(1-x^3/3)*(1x^4/4)*(2-x^5/5)*…)
Q(x,y)=y/(1-x)+y^2/。。。
P(x)=1+x+3*x^2/2!+11*x^3/3!+56*x^4/4!+324*x^5/5!+2324*x^6/6!+18332*x^7/7!+167544*x^8/8!+。。。