TITLE: Tensor powers of the standard representation
QUESTION [14 upvotes]: Consider $V_{(n-1, 1)}$, the $n-1$ dimensional irreducible representation of $S_n$, i.e. the "standard" or "defining" representation.  Is there a nice formula for how the $k$-th tensor power of $V_{(n-1, 1)}$ decomposes into irreps?

REPLY [6 votes]: The problem has been solved in the reference indicated in the comment
by Vasu Vineet, namely:
"Combinatorial Operators for Kronecker Powers of Representations of Sn" by
Alain Goupil and Cedric Chauve. However, one cannot say that the formulas in Propositions 1 and 2 of this paper are "nice".