此三角形开始于:
1;
1, 1;
1, 3, 1;
1, 6, 12, 1;
1, 10, 71, 76, 1;
1, 15, 281, 2153, 701, 1;
1, 21, 861, 29166, 129509, 8477, 1;
1, 28, 2212, 244725, 7664343, 12391414, 126126, 1;
1, 36, 4998, 1477391, 218030412, 3875325345, 1699148352, 2223278, 1;
1, 45, 10242, 7017577, 3748460115, 448713017405, 3284369541969, 315158247170, 45269999, 1; ...
...
通用公式:A(x,y)=1+(1+y)*x+(1+3*y+y^2)*x^2+(1+6*y+12*y^2+y^3)*x^3+(1+10*y+71*y^2+76*y^3+y^4)*x*4+(1+15*y+281*y^2+2153*y^3+701*y^4+y^5)*x_5+。。。
g.f.的对数等于级数:
对数(A(x))=(1+x)*x
+(1+2^2*x+x^2)*x^2/2
+(1+3^2*y+3^3*y^2+y^3)*x^3/3
+(1+4^2*y+6^3*y^2+4^4*y^3+x^4)*x^4/4
+(1+5^2*y+10^3*y^2+10^4*y^3+5^5*y^4+y^5)*x^5/5
+(1+6^2*y+15^3*y^2+20^4*y^3+15^5*y^4+6^6*y^5+y^6)*x^6/6+。。。