通用公式:A(x)=1+x+3*x^2+10*x^3+43*x^4+172*x^5+852*x^6+3719*x^7+。。。
G.f.:A(x)=exp(总和{n>=1}A203265型(n) *x^n/n),
其中A(x)=exp(总和{n>=1}G_n(x^n)^2*x^n/n)
和G_n(x)=exp(和{k>=1}A203265型(n*k)*x^k/k),开始于:
G_1(x)=A(x);
G_2(x)=1+5*x+75*x^2+1518*x^3+34663*x^4+867760*x^5+。。。;
G_3(x)=1+22*x+2019*x^2+214648*x^3+31221037*x^4+。。。;
G_4(x)=1+125*x+59771*x^2+40659310*x^3+31438395303*x^4+。。。;
G_5(x)=1+576*x+1760688*x^2+6380121685*x^3+。。。;
G_6(x)=1+3554*x+57073923*x^2+1295238092004*x^3+。。。;
G_7(x)=1+16843*x+1719312892*x^2+21211623589394*x^3+。。。;
G_8(x)=1+103917*x+56284535547*x^2+44125115136389518*x^3+。。。;
...
此外,G_n(x^n)=Product_{k=0..n-1}A(u^k*x),其中u=单位的第n个根:
G_2(x^2)=A(x)*A(-x);
G_3(x^3)=A(x)*A(u*x)*A(u^2*x),其中u=exp(2*Pi*I/3);
G_4(x^4)=A(x)*A(u*x)*A(u^2*x)*A(u^3*x)其中u=exp(2*Pi*I/4);
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A203265型= [1,5,22,125,576,3554,16843,103917,521338,3189600,...].