  Consider generalizations of the boundary singularities B_n of the functions
on the real line to the case where the boundary consists of a finite number of
l points. These singularities B_n^l could also arise in higher dimensional
case, when the boundary is an immersed hypersurface. We obtain a particular
recurrent equation on the numbers of connected components of very nice
M-morsification spaces of the multiboundary singularities B_n^l. This helps us
to express the numbers K_n^l (for l=2,3,4...) by Bernoulli-Euler numbers. We
also find the corresponding generating functions.
