Question Number 104607 by ~blr237~ last updated on 22/Jul/20
$$\:{if}\:\:\:{a}_{\mathrm{0}} =\mathrm{1}\:\:\:,\:\forall\:{n}\geqslant\mathrm{1}\:\:\:\:\:\underset{{p}=\mathrm{0}} {\overset{{n}} {\sum}}\:\frac{{a}_{{n}−{p}} }{\left({p}+\mathrm{1}\right)!}=\mathrm{0}\: \\ $$$${explicit}\:\:{a}_{{n}} \:\:{in}\:{terms}\:{of}\:{n}\: \\ $$