A note on the sums of powers of consecutive q-integers
  In this paper we construct the q-analogue of Barnes' Bernoulli numbers and plynomials of degree 2, which is an answer to a part of Schlosser's question. Finally, we treat the q-analogue of the sums of powers of consecutive integrs. 
Y. Simsek, D. Kim, T. Kim, S.-H. Rim