That's one odd mountain!

05AB1E, 54 52 47 46 bytes

ÅɹL£D€g__ÏRv"/ \ "yg×N·©úˆyvy4yg-ð×}J®>úˆ}¯R»

Try it online!

Explanation

                                                # implicit input n
ÅÉ                                              # push a list of uneven numbers up to input
  ¹L£                                           # divide into sublists of length 1,2,3...n
     D€g__Ï                                     # remove empty sublists
           R                                    # reverse list
            v                                   # for each sublist
             "/ \ "                             # push the string "/ \ "
                   yg×                          # repeat it len(sublist) times
                      N·©ú                      # prepend (sublist index)*2 spaces
                          ˆ                     # add to global list
                           yv                   # for each number in sublist
                             y4yg-ð×            # prepend spaces until length is 4
                                    }           # end inner loop
                                     J          # join to string
                                      ®>ú       # prepend (sublist index)*2+1 spaces
                                         ˆ      # add to global list
                                          }     # end outer loop
                                           ¯    # push global list
                                            R   # reverse it
                                             »  # join rows by space and columns by newline
                                                # implicitly print

I could have saved 5 bytes with ÅɹL£D€g__ÏRv"/ \ "yg×N·©úˆy4jJðÛ®>úˆ}¯R» if only I'd pushed that bugfix for j I wrote several weeks ago :/

Batch, 335 bytes

@echo off
set i=
set/ac=w=0
:l
set i=  %i%
set/aw+=2,c+=w
if %c% lss %1 goto l
set s=
set t=
set/ac=w=1
for /l %%a in (1,2,%1) do call:c %%a
echo  %s%
echo%t%
exit/b
:c
if not %c%==0 goto g
echo%i%%s%
set i=%i:~2%
echo%i%%t%
set s=
set t=
set/aw+=1,c=w
:g
set n=%1   (three trailing spaces)
set s=%s%%n:~0,4%
set t=%t% / \
set/ac-=1

Python 2, 160 149 143 bytes

^{Thanks TFeld for saving 11 bytes and Artyer for saving 6 bytes}

x=range(1,input()+1,2);y=[];i=1
while x:y+=[''.join('%-4d'%j for j in x[:i]),'/ \ '*len(x[:i])];x=x[i:];i+=1
while y:print' '*~-len(y)+y.pop(0)