Editing Euler numbers (section)

=== In terms of Stirling numbers of the second kind ===
The following two formulas express the Euler numbers in terms of [[Stirling numbers of the second kind]]:<ref>{{cite journal | first1=Sumit Kumar | last1= Jha | title=A new explicit formula for Bernoulli numbers involving the Euler number | journal=Moscow Journal of Combinatorics and Number Theory | volume=8 | issue=4 | pages=385–387 | year=2019 | url= https://projecteuclid.org/euclid.moscow/1572314455| doi= 10.2140/moscow.2019.8.389 | s2cid= 209973489 }}</ref><ref>{{cite web |url=https://osf.io/smw7h/ |title=A new explicit formula for the Euler numbers in terms of the Stirling numbers of the second kind |last=Jha |first=Sumit Kumar |date= 15 November 2019}}</ref>

:<math> E_{n}=2^{2n-1}\sum_{\ell=1}^{n}\frac{(-1)^{\ell}S(n,\ell)}{\ell+1}\left(3\left(\frac{1}{4}\right)^{\overline{\ell\phantom{.}}}-\left(\frac{3}{4}\right)^{\overline{\ell\phantom{.}}}\right), </math>
:<math> E_{2n}=-4^{2n}\sum_{\ell=1}^{2n}(-1)^{\ell}\cdot \frac{S(2n,\ell)}{\ell+1}\cdot \left(\frac{3}{4}\right)^{\overline{\ell\phantom{.}}},</math>

where <math> S(n,\ell) </math> denotes the [[Stirling numbers of the second kind]], and <math> x^{\overline{\ell\phantom{.}}}=(x)(x+1)\cdots (x+\ell-1) </math> denotes the [[Falling and rising factorials|rising factorial]].