伯努利数
\[S_p(n)=\Sigma_{k=0}^nk^p\\
G(z,n)=\Sigma_{p=0}^{\infty}Sp(n)/p!z^p=\Sigma_{k=0}^n\Sigma_{p=0}^{\infty}(kz)^p/p!\\
G(z,n)=\Sigma_{k=0}^ne^{kz}=(e^{(n+1)z}-1)/(e^z-1)\\
z/(e^z-1)=\Sigma_{k=0}^{\infty}B_k/k!*z^k\\
(e^{(n+1)z}-1)/z=(n+1)\Sigma_{k=0}^{\infty}((n+1)z)^k/(k+1)/k!\\
G(z,n)=\Sigma_{k=0}^{\infty}z^k/k!(n+1)\Sigma_{j=0}^{k}C_k^jBj*(n+1)^{k-j}/(k-j+1)\\
Sp(n) = (n+1)\Sigma_{j=0}^pC_p^jB_j*(n+1)^{p-j}/(p-j+1)\\
B_0=1, B_1=-1/2, B_2=1/6, B_3=0, B_4=-1/30\\
S_2(n)=(n+1)^2/3-(n+1)/2+1/6=(n+1)^3/3-(n+1)^2/2+(n+1)/6\\
S_1(n)=(n+1)^2/2-(n+1)/2=(n+1)*n/2
\]