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A160185 Triangle read by rows, (1 / ((-1)*A129184 * A007318 + I)) - I, I = Identity matrix. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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: A242431 A349934 A188416 * A283424 A188392 A143409

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

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Last modified August 16 20:45 EDT 2022. Contains 356169 sequences. (Running on oeis4.)