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

Author

Paul Barry, Feb 01 2010

Keywords

• nonn
• tabl

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.

Examples

			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;
		

Links

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