A144025 Eigentriangle by rows, A001006(n-k)*A005773(k); 0<=k<=n.

1, 1, 1, 2, 1, 2, 4, 2, 2, 5, 9, 4, 4, 5, 13, 21, 9, 8, 10, 13, 35, 51, 21, 18, 20, 26, 35, 96, 127, 51, 42, 45, 52, 70, 96, 267, 323, 127, 102, 105, 117, 140, 192, 267, 750, 835, 323, 254, 255, 273, 315, 384, 534, 750, 2123, 2188, 835, 646, 635, 663, 735, 864, 1068, 1500, 2123, 6046

Offset: 0

Author

Gary W. Adamson, Sep 07 2008

Keywords

• nonn
• tabl

Comments

Left border = Motzkin numbers, A001006.

Right border = A005773.

Row sums = A005773 shifted: (1, 2, 5, 13, 35, 96, 267,...).

Sum of n-th row terms = rightmost term of next row.

Examples

			First few rows of the triangle =
    1;
    1,   1;
    2,   1,   2;
    4,   2,   2,   5;
    9,   4,   4,   5,  13;
   21,   9,   8,  10,  13,  35;
   51,  21,  18,  20,  26,  35,  96;
  127,  51,  42,  45,  52,  70,  96, 267;
  323, 127, 102, 105, 117, 140, 192, 267, 750;
  835, 323, 254, 255, 273, 315, 384, 534, 750, 2123;
  ...
Row 3 = (4, 2, 2, 5) = termwise product of (4, 2, 1, 1) and the first 4 terms of A005773: (1, 1, 2, 5) = (4*1, 2*1, 1*2, 1*5). (4, 2, 1, 1) = the first 4 terms of A001066, reversed.
		

Crossrefs

Cf. A001066, A005773.

Formula

Eigentriangle by rows: T(n,k) = A001006(n-k)*A005773(k); 0<=k<=n.

Extensions

a(53) corrected by Georg Fischer, Apr 29 2025