User:Christopher Ernst

I am a graduate student at Rowan University. I also teach high school in NJ, primarily Algebra 1 and Algebra 2. I have recently started researching Bernoulli Numbers and Generalized Bernoulli Numbers. My interest is in finding convolution formulas for particular power series coefficients generated by exponential functions of the form $(x^{n}/n!)/e^{x}-1-x-...-(x^{(n-1)})/(n-1)!$. I am also interested in much of the work done on alternating permutations as well as much of what Carlitz named "up-up-...-up-down" permutations which have sequentially $n-1$ ascents and 1 descent. These have been shown to be a generalization of Euler Numbers.