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 A064191 Triangle T(n,k) (n >= 0, 0 <= k <= n) generalizing Motzkin numbers. 1

%I

%S 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,

%T 76,30,25,9,4,1,323,127,196,76,69,25,14,4,1,835,323,512,196,189,69,44,

%U 14,5,1,2188,835,1353,512,518,189,133,44,20,5,1,5798,2188,3610,1353

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

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

%C A number triangle with repeated columns of A064189. Production matrix is A070909 (without first term ). [From _Philippe DelĂ©ham_, Dec 02 2009]

%H J. L. Arregui, <a href="http://arXiv.org/abs/math.NT/0109108">Tangent and Bernoulli numbers</a> related to Motzkin and Catalan numbers by means of numerical triangles.

%F 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

%e 1; 1,1; 2,1,1; 4,2,2,1; ...

%Y First column gives A001006.

%K nonn,tabl,easy

%O 0,4

%A _N. J. A. Sloane_, Sep 21 2001

%E More terms from _David Wasserman_, Jul 15 2002

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Last modified January 19 20:01 EST 2019. Contains 319309 sequences. (Running on oeis4.)