title: What is the time complexity of T(n) = (T(n-1) + n!)?
body: <blockquote>
  <p>Let function F is recursive and has running time of F(k) is T(k).</p>
  <p>F(k) calls F(k-1) once, and does operations which run in O(n!)</p>
  <p>F(0) is a base case, and it runs in constant time.</p>
  </blockquote>
  <p>In my honest opinion,
  I thought that <code>T(n) = T(0) + (1! + 2! + ... + n!)</code>so
  it would be <code>T(n) &lt;= (n! + n! + ... + n!) for n &gt;=1</code>.
  thus <code>O((n+1)!)</code>.</p>
  <p>but I cannot be sure that this is enough bound.
  is it a enough analysis? and Is there any method I can test?
  (this algorithm is not quite practical but of curiosity.)</p>