On Generatingfunctionology of Lichtenberg sequence

Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. In this paper, we develop some important generating functions of the well-known Lichtenberg numbers. Some generating functions not known in the literature are discussed for l2n, l2n+1, lnln+1, and [ln]2, where ln is the nth Lichtenberg number. Using these generating functions, some convolution formulas that include this sequence are derived. Finally, we find some closed formulas for the sums of the square terms of the Lichtenberg numbers. The closed formulas presented here have many applications due to the simplicity of their presentation.