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A064191 Triangle T(n,k) (n >= 0, 0 <= k <= n) generalizing Motzkin numbers. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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 ). [From 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(T(n-1, k) : k = 0, ..., n-1). For k even, 0 < k <= n, T(n, k) = sum(T(n-1, j) : j = k-1, ..., n-1). For k odd, 0 < k <= n, T(n, k) = T(n-1, k-1). - David Wasserman, Jul 15 2002

EXAMPLE

1; 1,1; 2,1,1; 4,2,2,1; ...

CROSSREFS

First column gives A001006.

Sequence in context: A029268 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

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Last modified September 21 02:16 EDT 2018. Contains 315247 sequences. (Running on oeis4.)