Understanding PCB layer stack-up shorthand notation [2:(1(2+345*67)*16):7]
I'm reposting this from an old answer. I'm not sure this is a duplicate, because the old question specifically asks about Eagle CAD layers. 

The description on the notation is below. However, it appears the notation you got is flawed. The presence of the numbers '345' and '67' can't be correct.

It doesn't seem unreasonable to assume the '345' is '3*4*5' and the same for '67' being '6*7'. The corrected specification is:


  [2:(1*(2+3*4*5*6*7)*16):7]


If true, your stack up looks like this:



There are blind, buried, and standard vias.



From the EAGLE help file, (which uses the same layer notation you're dealing with):


  Layers
  
  The Layers tab defines which signal layers the board actually uses,
  how thick the copper and isolation layers are, and what kinds of vias
  can be placed (note that this applies only to actual vias; so even if
  no via from layer 1 to 16 has been defined in the layer setup, pads
  will always be allowed). 
  
  The layer setup is defined by the string in the "Setup" field. This
  string consists of a sequence of layer numbers, separated by one of
  the characters '*' or '+', where '*' stands for core material (also
  known as FR4 or something similar) and '+' stands for prepreg (or any
  other kind of isolation material). The actual core and prepreg
  sequence has no meaning to EAGLE other than varying the color in the
  layer display at the top left corner of this tab (the actual
  multilayer setup always needs to be worked out with the board
  manufacturer). The vias are defined by enclosing a sequence of layers
  with (...). So the setup string 
  
  (1*16)
  
  would mean a two layer board, using layers 1 and 16 and vias going
  through the entire board (this is also the default value). When
  building a multilayer board the setup could be something like 
  
  ((1*2)+(15*16))
  
  which is a four layer board with layer pairs 1/2 and 15/16 built on
  core material and vias drilled through them, and finally the two layer
  pairs pressed together with prepreg between them, and vias drilled all
  the way through the entire board. Besides vias that go through an
  entire layer stack (which are commonly referred to as buried vias in
  case they have no connection to the Top and Bottom layer) there can
  also be vias that are not drilled all the way through a layer stack,
  but rather end at a layer inside that stack. Such vias are known as
  blind vias and are defined in the "Setup" string by enclosing a
  sequence of layers with [t:...:b], where t and b are the layers up to
  which that via will go from the top or bottom side, respectively. A
  possible setup with blind vias could be 
  
  [2:1+((2*3)+(14*15))+16:15]
  
  which is basically the previous example, with two additional outer
  layers that are connected to the next inner layers by blind vias. It
  is also possible to have only one of the t or b parameters, so for
  instance  
  
  [2:1+((2*3)+(15*16))]
  
  would also be a valid setup. Finally, blind vias are not limited to
  starting at the Top or Bottom layer, but may also be used in inner
  layer stacks, as in 
  
  [2:1+[3:2+(3*4)+5:4]+16:5]
  
  A blind via from layer a to layer b also implements all possible blind
  vias from layer a to all layers between layers a and b, so 
  
  [3:1+2+(3*16)]
  
  would allow blind vias from layer 1 to 2 as well as from 1 to 3.