Sum of an infinite series

Calculus Level 3

\[\frac 1{3\times{0!}}+\frac 1{4\times{1!}}+\frac 1{5\times{2!}}+\frac 1{6\times{3!}}+\frac 1{7\times{4!}}+\cdots=?\]

Report your answer to 5 places after decimal