A154558 Triangle read by rows: binomial(n-1,k-1)*A001006(k).

1, 1, 2, 1, 4, 4, 1, 6, 12, 9, 1, 8, 24, 36, 21, 1, 10, 40, 90, 105, 51, 1, 12, 60, 180, 315, 306, 127, 1, 14, 84, 315, 735, 1071, 889, 323, 1, 16, 112, 504, 1470, 2856, 3556, 2584, 835, 1, 18, 144, 756, 2646, 6426, 10668, 11628, 7515, 2188

Offset

1,3

Links

Table of n, a(n) for n=1..55.

Formula

Binomial transform of a diagonalized version of the Motzkin sequence:

(A001006 (1, 2, 4, 9, 21, 51,...) as the main diagonal and the rest zeros.)

T(n,n) = A001006(n).

Example

First few rows of the triangle =
1;
1, 2;
1, 4, 4;
1, 6, 12, 9;
1, 8, 24, 36, 21;
1, 10, 40, 90, 105, 51;
1, 12, 60, 180, 315, 306, 127;
1, 14, 84, 315, 735, 1071, 889, 323;
1, 16, 112, 504, 1470, 2856, 3556, 2584, 835;
1, 18, 144, 756, 2646, 6426, 10668, 11628, 7515, 2188;
1, 20, 180, 1080, 4410, 12852, 26670, 38760, 37575, 21880, 5798;
...

Crossrefs

Cf. A001006, A000245 (row sums), A005843 (column k=2), A046092 (column k=3).

Sequence in context: A133544 A303872 A013609 * A220836 A008572 A209150

Adjacent sequences: A154555 A154556 A154557 * A154559 A154560 A154561

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Jan 11 2009

Status

approved