  In a companion paper, we introduced raising operator series called
Catalanimals. Among them are Schur Catalanimals, which represent Schur
functions inside copies $\Lambda (X^{m,n})\subset \mathcal{E} $ of the algebra
of symmetric functions embedded in the elliptic Hall algebra $\mathcal{E} $ of
Burban and Schiffmann.
  Here we obtain a combinatorial formula for symmetric functions given by a
class of Catalanimals that includes the Schur Catalanimals. Our formula is
expressed as a weighted sum of LLT polynomials, with terms indexed by
configurations of nested lattice paths called nests, having endpoints and
bounding constraints controlled by data called a den.
  Applied to Schur Catalanimals for the alphabets $X^{m,1}$ with $n=1$, our
`nests in a den' formula proves the combinatorial formula conjectured by Loehr
and Warrington for $\nabla^m s_{\mu }$ as a weighted sum of LLT polynomials
indexed by systems of nested Dyck paths. When $n$ is arbitrary, our formula
establishes an $(m,n)$ version of the Loehr-Warrington conjecture.
  In the case where each nest consists of a single lattice path, the nests in a
den formula reduces to our previous shuffle theorem for paths under any line.
Both this and the $(m,n)$ Loehr-Warrington formula generalize the $(km,kn)$
shuffle theorem proven by Carlsson and Mellit (for $n=1$) and Mellit. Our
formula here unifies these two generalizations.
