B(k):=IF(k=0,1,IF(k=1,-1/2,-k*ZETA(1-k)))

;User=Simp(User)
VECTOR(B(2*k+1),k,1,12)=[0,0,0,0,0,0,0,0,0,0,0,0]

S(k,x):=k*SUM(p^(k-1),p,1,x-1)

;User=Simp(User)
VECTOR(DIF(S(k,x),x)-k*(S(k-1,x)+B(k-1)),k,3,12)=[0,0,0,0,0,0,0,0,0,0]