symmetric monoidal (∞,1)-category of spectra
An ordinary (∞,1)-operad $\mathcal{O}$ is equivalently incarnated as its (∞,1)-category of operators $\mathcal{O}^\otimes \to FinSet_*$, which in particular has the property that $\mathcal{O}^{\otimes}_{\langle 0\rangle} \simeq *$.
A generalized $(\infty,1)$-operad is like an (∞,1)-category of operators only that this condition is dropped and
is allowed to be any (∞,1)-category.
It is essentially the same kind of data as a family of (∞,1)-operads (see there for more) parameterized over $\mathcal{C}$.
Section 2.3.2 of
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