Bernoulli-Identity and related sequences

[Gottfried Helms]

Just discovered an interesting Bernoulli-identity:

       2n
  0 = sum (-1)^k binomial(n,k-n) * b(k-1)*k
      k=n

(where b1 = +1/2)

The interesting part for seqfan-list may be the
discussion of a relation of the basic numbertheoretic
sequences in the light of the eigenvectors of the
binomial matrix.

Because of trouble with the ascii-chars in this
list I prepared a pdf:

 http://go.helms-net.de/math/bernoulli/GeneralizedBernoulliRecursion.pdf

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Then today I found an article of Zhi Wei Sun,
where he mentions that this identity was already
found by von Ettinghausen in 1827 and then
1995 rediscovered by M. Kaneko. But from the
Z. W. Sun-article I think, my approach shows a path
to a wider generality, so it may be of interest.


I would like to get comments -

Regards

Gottfried Helms