Tropp–Webber numerical inequality (B.8): $\big(1+\frac{2p}{x+1-2p}\big)\Gamma(x+2)^{-2p/(x+1)}\le (e/x)^{2p}$ for $1\le p\le 18$, $x\ge 2p$

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Tropp–Webber numerical inequality (B.8): $\big(1+\frac{2p}{x+1-2p}\big)\Gamma(x+2)^{-2p/(x+1)}\le (e/x)^{2p}$ for $1\le p\le 18$, $x\ge 2p$ · Prove2Me