Geodesic
A short proof of Carlitz's Bernoulli number identity
Journal of integer sequences, Tome 17 (2014) no. 4
For an identity related to Bernoulli numbers, stated by Carlitz, rediscovered and reproved by various researchers, an extremely short and direct proof is provided which uses a bivariate exponential function.
Classification : 11B68, 05A10, 11B65
Keywords: Bernoulli number, exponential generating function 
@article{JIS_2014__17_4_a4,
     author = {Prodinger,  Helmut},
     title = {A short proof of {Carlitz's} {Bernoulli} number identity},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {4},
     zbl = {1353.11041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_4_a4/}
}
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Prodinger,  Helmut. A short proof of Carlitz's Bernoulli number identity. Journal of integer sequences, Tome 17 (2014) no. 4. http://geodesic.mathdoc.fr/item/JIS_2014__17_4_a4/