\begin{definition}[Definition:Bernoulli Numbers/Archaic Form/Sequence]
The sequence of old style Bernoulli numbers begins:
{{begin-eqn}}
{{eqn | l = B_1^*
      | r = \dfrac 1 6
      | rr= = B_2
      | c = 
}}
{{eqn | l = B_2^*
      | r = \dfrac 1 {30}
      | rr= = -B_4
      | c = 
}}
{{eqn | l = B_3^*
      | r = \dfrac 1 {42}
      | rr= = B_6
      | c = 
}}
{{eqn | l = B_4^*
      | r = \dfrac 1 {30}
      | rr= = -B_8
      | c = 
}}
{{eqn | l = B_5^*
      | r = \dfrac 5 {66}
      | rr= = B_{10}
      | c = 
}}
{{eqn | l = B_6^*
      | r = \dfrac {691} {2730}
      | rr= = -B_{12}
      | c = 
}}
{{eqn | l = B_7^*
      | r = \dfrac 7 6
      | rr= = B_{14}
      | c = 
}}
{{eqn | l = B_8^*
      | r = \dfrac {3617} {510}
      | rr= = -B_{16}
      | c = 
}}
{{eqn | l = B_9^*
      | r = \dfrac {43 \, 867} {798}
      | rr= = B_{18}
      | c = 
}}
{{eqn | l = B_{10}^*
      | r = \dfrac {174 \, 611} {330}
      | rr= = -B_{20}
      | c = 
}}
{{eqn | l = B_{11}^*
      | r = \dfrac {854 \, 513} {138}
      | rr= = B_{22}
      | c = 
}}
{{eqn | l = B_{12}^*
      | r = \dfrac {236 \, 364 \, 091} {2730}
      | rr= = -B_{24}
      | c = 
}}
{{end-eqn}}
where $B_2, B_4, \ldots$ are the standard form Bernoulli numbers.
{{OEIS-Denominators|A002445}}
\end{definition}