A two-sided Faulhaber-like formula involving Bernoulli polynomials

Kavli Affiliate: J. S. Villasenor

| First 5 Authors: Fernando Barbero G., Juan Margalef-Bentabol, Eduardo J. S. VillaseƱor, ,

| Summary:

We give a new identity involving Bernoulli polynomials and combinatorial
numbers. This provides, in particular, a Faulhaber-like formula for sums of the
form $1^m (n-1)^m + 2^m (n-2)^m + cdots + (n-1)^m 1^m$ for positive integers
$m$ and $n$.

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