On the Brousseau sums ${\sum }_{i=1}^n{i}^p{F}_i$

Abstract

We start with new convolution formulas for $F_n-n^p$ involving only the binomial coefficients. Then, we use those to find direct formulas for the sums ${\sum }_{i=1}^n{i}^p{F}_{n-i}$ and ${\sum }_{i=1}^n{i}^p{F}_i$, and we show how our formulas connect to work in earlier papers by Ledin, Brousseau, Zeitlin, Adegoke, Shannon and Ollerton, and Kinlaw, Morris, and Thiagarajan.

17 pages. Currently under review for publication