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Given $(a_i \in \mathbb{N})$$(a_n \in \mathbb{N})$, when is there a monadmonad$T$ on $\mathrm{FinSet}$ such that
$$
| T(i) | = a_i\quad\forall i\:?
$$$$
| T(n) | = a_n\quad\forall n\in \mathbb{N}\:?
$$
Given $(a_i \in \mathbb{N})$, when is there a monad$T$ on $\mathrm{FinSet}$ such that
$$
| T(i) | = a_i\quad\forall i\:?
$$
Given $(a_n \in \mathbb{N})$, when is there a monad$T$ on $\mathrm{FinSet}$ such that
$$
| T(n) | = a_n\quad\forall n\in \mathbb{N}\:?
$$
