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, 720, 2123, 2188, 835, 646, 635, 663, 735, 864, 1068

Offset

0,4

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.

Links

Table of n, a(n) for n=0..62.

Formula

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

Example

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, 720, 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.

Sequence in context: A114929 A247321 A152251 * A058573 A184990 A206299

Adjacent sequences: A144022 A144023 A144024 * A144026 A144027 A144028

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 07 2008

Status

approved