  We present comprehensive observations and analysis of the energetic
H-stripped SN 2016coi (a.k.a. ASASSN-16fp), spanning the $\gamma$-ray through
optical and radio wavelengths, acquired within the first hours to $\sim$420
days post explosion. Our campaign confirms the identification of He in the SN
ejecta, which we interpret to be caused by a larger mixing of Ni into the outer
ejecta layers. From the modeling of the broad bolometric light curve we derive
a large ejecta mass to kinetic energy ratio ($M_{\rm{ej}}\sim
4-7\,\rm{M_{\odot}}$, $E_{\rm{k}}\sim 7-8\times 10^{51}\,\rm{erg}$). The small
[\ion{Ca}{ii}] \lam\lam7291,7324 to [\ion{O}{i}] \lam\lam6300,6364 ratio
($\sim$0.2) observed in our late-time optical spectra is suggestive of a large
progenitor core mass at the time of collapse. We find that SN 2016coi is a
luminous source of X-rays ($L_{X}>10^{39}\,\rm{erg\,s^{-1}}$ in the first
$\sim100$ days post explosion) and radio emission ($L_{8.5\,GHz}\sim7\times
10^{27}\,\rm{erg\,s^{-1}Hz^{-1}}$ at peak). These values are in line with those
of relativistic SNe (2009bb, 2012ap). However, for SN 2016coi we infer
substantial pre-explosion progenitor mass-loss with rate $\dot M \sim
(1-2)\times 10^{-4}\,\rm{M_{\odot}yr^{-1}}$ and a sub-relativistic shock
velocity $v_{sh}\sim0.15c$, in stark contrast with relativistic SNe and similar
to normal SNe. Finally, we find no evidence for a SN-associated shock breakout
$\gamma$-ray pulse with energy $E_{\gamma}>2\times 10^{46}\,\rm{erg}$. While we
cannot exclude the presence of a companion in a binary system, taken together,
our findings are consistent with a massive single star progenitor that
experienced large mass loss in the years leading up to core-collapse, but was
unable to achieve complete stripping of its outer layers before explosion.
