One sign flips
From the first convention to the second
B
n
+
= (−1)
n
B
n
−
indices 0 to 8 shown
Odd n above 1: the value is 0, and 0 × (−1) is still 0.
Even n: (−1)
n
is +1, so the value is unchanged.
They differ only at n = 1: −1/2 becomes +1/2.