A172380 Eigentriangle of Catalan triangle A033184.

1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 5, 10, 6, 1, 0, 14, 36, 31, 10, 1, 0, 42, 137, 156, 75, 15, 1, 0, 132, 544, 787, 510, 155, 21, 1, 0, 429, 2235, 4017, 3331, 1380, 287, 28, 1, 0, 1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1, 0, 4862, 40876, 109486, 136921, 90665

Offset

0,8

Comments

Row sums are A091768.

Production matrix of inverse is matrix with general term (-1)^(n-k+1)C(k,n-k+1).

Diagonal sums are A172382. Product of A033184 and A172380 is the matrix A172381.

Links

Table of n, a(n) for n=0..60.

Paul Barry, Invariant number triangles, eigentriangles and Somos-4 sequences, arXiv preprint arXiv:1107.5490 [math.CO], 2011.

Example

Triangle begins
  1;
  0,    1;
  0,    1,    1;
  0,    2,    3,     1;
  0,    5,   10,     6,     1;
  0,   14,   36,    31,    10,     1;
  0,   42,  137,   156,    75,    15,    1;
  0,  132,  544,   787,   510,   155,   21,   1;
  0,  429, 2235,  4017,  3331,  1380,  287,  28,  1;
  0, 1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1;
Production matrix of inverse is
  0,  1;
  0, -1,  1;
  0,  0, -2,  1;
  0,  0,  1, -3,  1;
  0,  0,  0,  3, -4,   1;
  0,  0,  0, -1,  6,  -5,   1;
  0,  0,  0,  0, -4,  10,  -6,   1;
  0,  0,  0,  0,  1, -10,  15,  -7,   1;
  0,  0,  0,  0,  0,   5, -20,  21,  -8,  1;
  0,  0,  0,  0,  0,  -1,  15, -35,  28, -9,   1;
  0,  0,  0,  0,  0,   0,  -6,  35, -56, 36, -10, 1;

Crossrefs

Sequence in context: A081247 A298753 A173050 * A144633 A352366 A264428

Adjacent sequences: A172377 A172378 A172379 * A172381 A172382 A172383

Keyword

nonn,tabl

Author

Paul Barry, Feb 01 2010

Status

approved