L.g.f.:L(x)=x+3*x^2/2+7*x^3/3+19*x^4/4+26*x^5/5+75*x^6/6+。。。
哪里
L(x)=x*exp(1*x+3*x^2/2+4*x^3/3+7*x^4/4+6*x^5/5+…)+
x^2/2*经验(3*x^2+7*x^4/2+12*x^6/3+15*x^8/4+18*x^10/5+…)+
x^3/3*经验(4*x^3+12*x^6/2+13*x^9/3+28*x^12/4+24*x^15/5+…)+
x^4/4*exp(7*x^4+15*x^8/2+28*x^12/3+31*x^16/4+42*x^20/5+…)+
x^5/5*经验(6*x^5+18*x^10/2+24*x^15/3+42*x^20/4+31*x^25/5+…)+
x^6/6*出口(12*x^6+28*x^12/2+39*x^18/3+60*x^24/4+72*x^30/5+…)+
x^7/7*经验(8*x^7+24*x^14/2+32*x^21/3+56*x^28/4+48*x*^35/5+…)+
x^8/8*经验(15*x^8+31*x^16/2+60*x^24/3+63*x^32/4+90*x^40/5+…)+。。。
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等价地,L(x)=Sum_{n>=1}P_n(x^n)*x^n/n,其中
P_n(x)=exp(和{k>=1}σ(n*k)*x^k/k),开始于:
P_1(x)=1+x+2*x^2+3*x^3+5*x^4+7*x^5+11*x^6+15*x^7+。。。;
P_2(x)=1+3*x+8*x^2+19*x^3+41*x^4+83*x^5+161*x^6+。。。;
P_3(x)=1+4*x+14*x^2+39*x^3+101*x^4+238*x^5+533*x^6+。。。;
P_4(x)=1+7*x+32*x^2+119*x^3+385*x^4+1127*x^5+3057*x^6+。。。;
P_5(x)=1+6*x+27*x^2+98*x^3+315*x^4+917*x^5+2486*x^6+。。。;
P_6(x)=1+12*x+86*x^2+469*x^3+2141*x^4+8594*x^5+。。。;
P_7(x)=1+8*x+44*x ^2+192*x ^3+726*x ^4+2464*x ^5+。。。;
P_8(x)=1+15*x+128*x^2+815*x^3+4289*x^4+19663*x^5+。。。;
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