[seqfan] Number array not found in OEIS

[Gottfried Helms]

Seqfriends -

 I came across this number array (should be extended to infinity) by q-brackets/q-binomials
 to base 2 and cannot find a good description. Does someone know this array or has an
 idea how to decode?

   1    -1       1        -1            1            -1                 1                    -1
  -1     3      -7        15          -31            63              -127                   255
   1    -7      43      -211          931         -3907             16003                -64771
  -1    15    -211      2619       -26251        234795          -1985131              16323819
   1   -31     931    -26251       654811     -13255291         238658491           -4050110011
  -1    63   -3907    234795    -13255291     662827803      -26961325147          973958217435
   1  -127   16003  -1985131    238658491  -26961325147     2699483026843      -220115609012251
  -1   255  -64771  16323819  -4050110011  973958217435  -220115609012251

or perhaps better readable:
   1  -1   1  -1   1   -1     1      -1 ...
      -1   3  -7  15  -31    63    -127 ...
           1  -7  43 -211   931   -3907 ...
              -1  15 -211  2619  -26251 ...
                   1  -31   931  -26251 ...
                       -1    63   -3907 ...
                              1    -127 ...
                                     -1 ...
                                     ...

 Clearly the signs are not relevant here...

 Sincerely -

 Gottfried Helms