%I A064191
%S A064191 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 A064191 76,30,25,9,4,1,323,127,196,76,69,25,14,4,1,835,323,512,196,189,69,44,
%U A064191 14,5,1,2188,835,1353,512,518,189,133,44,20,5,1,5798,2188,3610,1353
%N A064191 Triangle T(n,k) (n >= 0, 0 <= k <= n) generalizing Motzkin numbers.
%C A064191 This triangle appears on page 9 of the linked reference and is defined 
               by Corollary 2.4.
%H A064191 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 A064191 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 (wasserma(AT)spawar.navy.mil), 
               Jul 15 2002
%e A064191 1; 1,1; 2,1,1; 4,2,2,1; ...
%Y A064191 First column gives A001006.
%Y A064191 Sequence in context: A156861 A122773 A029268 this_sequence A127420 A129033 
               A054090
%Y A064191 Adjacent sequences: A064188 A064189 A064190 this_sequence A064192 A064193 
               A064194
%K A064191 nonn,tabl,easy
%O A064191 0,4
%A A064191 N. J. A. Sloane (njas(AT)research.att.com), Sep 21 2001
%E A064191 More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jul 15 
               2002