In[]:=
p0[i_]:=Sum[
j
(-1)
2j-2
2
(Binomial[i+j-2,2j-2](2i-1)/(2j-1)),{j,1,i}]
p[i_,x_]:=Sum[
j
(-1)
2j-2
2
(Binomial[i+j-2,2j-2](2i-1)/(2j-1))
2j-1
x
,{j,1,i}]
In[]:=
N[p0[3]]
Out[]=
-1.
In[]:=
N[p[3,1]]
Out[]=
1.