You may also use [SAGE][1] , (for example, the  [Sage online notebook][2]
)

Example: 

   The Riemann curvature tensor $R$ lives in the space $Sym^2(\Lambda^2 V)$
(after identifying $V$ with $V^{\vee}$)

Decomposing it in Sage:

  $   s = SFASchur(QQ) $ 

(let s be the Schur functor) 


  $ s(\[2\])(s(\[1,1\])) $

(compute plethysm $ Sym^2 \Lambda^2 $)

> s[1, 1, 1, 1] + s[2, 2]  

-- i.e., $\Lambda^4 V + S_{\[2,2\]}$, as it should be 


$ s(\[3\])(s(\[1,1\]))

> s[1, 1, 1, 1, 1, 1] + s[2, 2, 1, 1] + s[3, 3]

-- though i understand that the explicit formula is better :)


  [1]: http://sagemath.org/
  [2]: https://sagenb.kaist.ac.kr/