All possible heaps

How many distinct (not necessarily binary) min-heaps can be constructed from the nodes with keys \(1,\ldots,999999\)?

Give the answer modulo \(10^{9}+7\).

Note:

Let be \(H_1, H_2\) two heaps: \(H_1 \neq H_2 \iff \exists uv \; \; \textbf{:} \; \; uv \in H_1 \land uv \notin H_2 \)


Inspiration.

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