  Let $H$ be a finite dimensional pointed rank one Hopf algebra of nilpotent
type. We first determine all finite dimensional indecomposable $H$-modules up
to isomorphism, and then establish the Clebsch-Gordan formulas for the
decompositions of the tensor products of indecomposable $H$-modules by virtue
of almost split sequences. The Green ring $r(H)$ of $H$ will be presented in
terms of generators and relations. It turns out that the Green ring $r(H)$ is
commutative and is generated by one variable over the Grothendieck ring
$G_0(H)$ of $H$ modulo one relation. Moreover, $r(H)$ is Frobenius and
symmetric with dual bases associated to almost split sequences, and its
Jacobson radical is a principal ideal. Finally, we show that the stable Green
ring, the Green ring of the stable module category, is isomorphic to the
quotient ring of $r(H)$ modulo the principal ideal generated by the projective
cover of the trivial module. It turns out that the complexified stable Green
algebra is a group-like algebra and hence a bi-Frobenius algebra.
