  We give an analog of a Chevalley-Serre presentation for the Lie superalgebras
W(n) and S(n) of Cartan type. These are part of a wider class of Lie
superalgebras, the so-called tensor hierarchy algebras, denoted W(g) and S(g),
where g denotes the Kac-Moody algebra A_r, D_r or E_r. Then W(A_{n-1}) and
S(A_{n-1}) are the Lie superalgebras W(n) and S(n). The algebras W(g) and S(g)
are constructed from the Dynkin diagram of the Borcherds-Kac-Moody
superalgebras B(g) obtained by adding a single grey node (representing an odd
null root) to the Dynkin diagram of g. We redefine the algebras W(A_r) and
S(A_r) in terms of Chevalley generators and defining relations. We prove that
all relations follow from the defining ones at level -2 and higher. The
analogous definitions of the algebras in the D- and E-series are given. In the
latter case the full set of defining relations is conjectured.
