  We derive closed-form expressions for all ingredients of the
Zamolodchikov-like recursion relation for general spinning conformal blocks in
3-dimensional conformal field theory. This result opens a path to efficient
automatic generation of conformal block tables, which has immediate
applications in numerical conformal bootstrap program. Our derivation is based
on an understanding of null states and conformally-invariant differential
operators in momentum space, combined with a careful choice of the relevant
tensor structures bases. This derivation generalizes straightforwardly to
higher spacetime dimensions d, provided the relevant Clebsch-Gordan
coefficients of Spin(d) are known.
