There is a non recursive formula for T(x,k)? - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: There is a non recursive formula for T(x,k)? (/showthread.php?tid=1278) There is a non recursive formula for T(x,k)? - marraco - 12/17/2020 Consider the tetration of the function $\vspace{15}{e^x}$ $^n(e^x)=(e^x)_1^{(e^x)_2^{(e^x)_2^{_..^{.e^x_n}}}}$ For a natural number n, the taylor series of that function is $^n(e^x)=\sum_{k=0}^{\infty}\frac{1}{k!}*T(n,k)*x^k$ where $\vspace{15}{T(n,k)}$ is the OEIS A210725; When k