A160185 Triangle read by rows, (1 / ((-1)*A129184 * A007318 + I)) - I, I = Identity matrix.

1, 2, 1, 5, 3, 1, 15, 9, 4, 1, 52, 31, 14, 5, 1, 203, 121, 54, 20, 6, 1, 877, 523, 233, 85, 27, 7, 1, 4140, 2469, 1101, 400, 125, 35, 8, 1, 21147, 12611, 5625, 2046, 635, 175, 44, 9, 1, 115975, 69161, 30846, 11226, 3488, 952, 236, 54, 10, 1

Offset

0,2

Comments

Inverse binomial transform of the triangle shifts to left (= adding I as right border, I = Identity matrix); resulting in reversed rows of A121207.

Left border = Bell numbers, A000110 = eigensequence of Pascal's triangle.

Successive columns from left to right = eigensequences of Pascal's triangle deleting columns one at a time.

Row sums of the triangle = A060719: (1, 3, 9, 29, 103, ...). - Gary W. Adamson, May 20 2013

From Gary W. Adamson, Jul 18 2019: (Start)

Rows are eigensequences of triangles exemplified by the following arrangement of binomial sequences. Example: row 5 is (1, 5, 14, 31, 52, 0, 0, 0, ...), the eigensequence of:

1;

4, 1;

6, 3, 1;

4, 3, 2, 1;

1, 1, 1, 1, 1;

... and the rest zeros.

Similarly, the production matrix for (1, 6, 20, 54, 121, 203, 0, 0, 0, ...) is:

1;

5, 1;

10, 4, 1;

10, 6, 3, 1;

5, 4, 3, 2, 1;

1, 1, 1, 1, 1, 1;

... and the rest zeros. (End)

Links

Table of n, a(n) for n=0..54.

Formula

Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix.

Equals reversal by rows of triangle A121207, then delete right border. A121207 begins: 1; 1, 1; 1, 1, 2 1, 1, 3, 5; ...

Example

First few rows of the triangle:
       1;
       2,     1;
       5,     3,     1;
      15,     9,     4,     1;
      52,    31,    14,     5,    1;
     203,   121,    54,    20,    6,   1;
     877,   523,   233,    85,   27,   7,   1;
    4140,  2469,  1101,   400,  125,  35,   8,  1;
   21147, 12611,  5625,  2046,  635, 175,  44,  9,  1;
  115975, 69161, 30846, 11226, 3488, 952, 236, 54, 10, 1;
  ...

Crossrefs

Cf. A121207, A124496, A186020.

Cf. A060719.

Sequence in context: A349934 A188416 A361654 * A283424 A188392 A356558

Adjacent sequences: A160182 A160183 A160184 * A160186 A160187 A160188

Keyword

nonn,tabl

Author

Gary W. Adamson, May 03 2009

Extensions

Corrected by Alois P. Heinz, Apr 18 2013

Status

approved