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Mathematics  2011 

A shortened recurrence relation for the Bernoulli numbers

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Abstract:

In this note, starting with a little-known result of Kuo, I derive a recurrence relation for the Bernoulli numbers $B_{2 n}$, $n$ being any positive integer. This new recurrence seems advantageous in comparison to other known formulae since it allows the computation of both $B_{4 n}$ and $B_{4 n +2}$ from only $B_0, B_2,..., B_{2n}$.

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