  Lie subalgebras of $ L = \mathfrak{g}(\!(x)\!) \times
\mathfrak{g}[x]/x^n\mathfrak{g}[x] $, complementary to the diagonal embedding
$\Delta$ of $ \mathfrak{g}[\![x]\!] $ and Lagrangian with respect to some
particular form, are in bijection with formal classical $r$-matrices and
topological Lie bialgebra structures on the Lie algebra of formal power series
$ \mathfrak{g}[\![x]\!] $. In this work we consider arbitrary subspaces of $ L
$ complementary to $\Delta$ and associate them with so-called series of type $
(n,s) $.
  We prove that Lagrangian subspaces are in bijection with skew-symmetric $
(n,s) $-type series and topological quasi-Lie bialgebra structures on $
\mathfrak{g}[\![x]\!] $. Using the classificaiton of Manin pairs we classify up
to twisting and coordinate transformations all quasi-Lie bialgebra structures.
  Series of type $ (n,s) $, solving the generalized Yang-Baxter equation,
correspond to subalgebras of $L$. We discuss their possible utility in the
theory of integrable systems.
