A064191 Triangle T(n,k) (n >= 0, 0 <= k <= n) generalizing Motzkin numbers.

1, 1, 1, 2, 1, 1, 4, 2, 2, 1, 9, 4, 5, 2, 1, 21, 9, 12, 5, 3, 1, 51, 21, 30, 12, 9, 3, 1, 127, 51, 76, 30, 25, 9, 4, 1, 323, 127, 196, 76, 69, 25, 14, 4, 1, 835, 323, 512, 196, 189, 69, 44, 14, 5, 1, 2188, 835, 1353, 512, 518, 189, 133, 44, 20, 5, 1, 5798, 2188, 3610, 1353

Offset: 0

Author

N. J. A. Sloane, Sep 21 2001

Keywords

• nonn
• tabl
• easy

Comments

This triangle appears on page 9 of the linked reference and is defined by Corollary 2.4.

A number triangle with repeated columns of A064189. Production matrix is A070909 (without first term). - Philippe Deléham, Dec 02 2009

Examples

			Triangle begins
  1;
  1, 1;
  2, 1, 1;
  4, 2, 2, 1; ...
		

Links

• J. L. Arregui, Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles.

Crossrefs

First column gives A001006.

Formula

T(n, 0) = Sum_{k=0..n-1} T(n-1, k). For k even, 0 < k <= n, T(n, k) = Sum_{j=k-1..n-1} T(n-1, j). For k odd, 0 < k <= n, T(n, k) = T(n-1, k-1). - David Wasserman, Jul 15 2002

Extensions

More terms from David Wasserman, Jul 15 2002