[seqfan] Re: Tabl formula?

[Richard Mathar]

http://list.seqfan.eu/pipermail/seqfan/2011-April/014747.html

With some experimentation, it seems that the n-th row can be characterized
by having an inverse binomial transform (note this is with an offet 0 
for the term that is actually defined with offset 1!) which is the 
integers counted backwards. So in the binomial base, the polynomials
might have simple coefficients:
                          "n=", 1, "terms=", [2, 3, 4]
                         "inverse binomial transform
                                   [2, 1, 0]

                        "n=", 2, "terms=", [3, 5, 8, 12]
                         "inverse binomial transform
                                  [3, 2, 1, 0]

                     "n=", 3, "terms=", [4, 7, 12, 20, 32]
                         "inverse binomial transform
                                [4, 3, 2, 1, 0]

                   "n=", 4, "terms=", [5, 9, 16, 28, 48, 80]
                         "inverse binomial transform
                               [5, 4, 3, 2, 1, 0]

                "n=", 5, "terms=", [6, 11, 20, 36, 64, 112, 192]
                         "inverse binomial transform
                             [6, 5, 4, 3, 2, 1, 0]

             "n=", 6, "terms=", [7, 13, 24, 44, 80, 144, 256, 448]
                         "inverse binomial transform
                            [7, 6, 5, 4, 3, 2, 1, 0]

          "n=", 7, "terms=", [8, 15, 28, 52, 96, 176, 320, 576, 1024]
                         "inverse binomial transform
                          [8, 7, 6, 5, 4, 3, 2, 1, 0]

       "n=", 8, "terms=", [9, 17, 32, 60, 112, 208, 384, 704, 1280, 2304]
                         "inverse binomial transform
                         [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]

   "n=", 9, "terms=", [10, 19, 36, 68, 128, 240, 448, 832, 1536, 2816, 5120]
                         "inverse binomial transform
                       [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]

"n=", 10, "terms=",
    [11, 21, 40, 76, 144, 272, 512, 960, 1792, 3328, 6144, 11264]
                         "inverse binomial transform
                     [11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]