binomial_combine_tensor
=======================

.. py:function:: t3toolbox.backend.sampling_derivatives.binomial_combine_tensor(order)

   .. code-block:: python

      def binomial_combine_tensor(
              order:  int,        # highest derivative order K
      ) -> NDArray:               # trs. shape=(order+1,order+1,order+1). trs[t,r,s] = C(t,r) if r+s==t else 0


   Binomial tensor driving every jet convolution.

   ``trs[t,r,s] = C(t,r)`` when ``r+s==t`` and ``0`` otherwise, so contracting it against the outer
   product of two jets reproduces ``sum_{r+s=t} C(t,r) (.)^(r) (.)^(s)`` -- the product rule on
   Taylor jets. Used by both the pushthrough (input jet, ``s in {0,1}`` -> slice ``[:, :, :2]``) and
   the combine (full ``s``). Pure structure (exact integer binomials), so always numpy -- it folds
   into the compiled program as a device constant on the jax path, like the uniform masks.