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

0,4

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

Links

Table of n, a(n) for n=0..69.

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

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

Example

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

Crossrefs

First column gives A001006.

Sequence in context: A347629 A176452 A244581 * A127420 A129033 A054090

Adjacent sequences: A064188 A064189 A064190 * A064192 A064193 A064194

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, Sep 21 2001

Extensions

More terms from David Wasserman, Jul 15 2002

Status

approved