Action of symmetric group

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Hello,

I am trying to understand of to use group action in sagemath, more specifically the action of symmetric group of size n, in order to count the number of isomorphism classes of simple undirected graphs. They are given by a symmetric unimodal sequence where the elements a_k are given by $$a_k = \mathfrak{S}_n \backslash S_k(S_2(V))\ ,$$ with $V$ the set of vertices and $S_k(V)$ the set of $k$-element submultiset of $V$.

I have an algorithm that gives me the size of $S_2(V)$ and $S_k(S_2(V))$ but I'm struggling with how to obtain $\mathfrak{S}_n \backslash S_k(S_2(V))$.

Any help welcome ! For more information about it I can send you my paper that contains more definitions, examples and proofs. Thank you very much !