Search: id:A059365
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%I A059365
%S A059365 0,0,1,0,1,1,0,2,2,1,0,5,5,3,1,0,14,14,9,4,1,0,42,42,28,14,5,1,
%T A059365 0,132,132,90,48,20,6,1,0,429,429,297,165,75,27,7,1,0,1430,1430,
%U A059365 1001,572,275,110,35,8,1,0,4862,4862,3432,2002,1001,429,154,44
%N A059365 Another version of the Catalan triangle: T(r,s) = binomial(2*r-s-1,r-1)-binomial(2*r-s-1,
               r), r>=0, 0<=s<=r.
%D A059365 F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 
               (1999) 73-112.
%H A059365 D. Callan, <a href="http://arXiv.org/abs/math.CO/0211380">A recursive 
               bijective approach to counting permutations...</a>
%H A059365 A. Robertson, D. Saracino and D. Zeilberger, <a href="http://arXiv.org/
               abs/math.CO/0203033">Refined restricted permutations</a>.
%F A059365 Essentially the same triangle as [0, 1, 1, 1, 1, 1, 1, ...] DELTA A000007, 
               where DELTA is Deleham's operator defined in A084938, but the first 
               term is T(0, 0)= 0.
%e A059365 0; 0,1; 0,1,1; 0,2,2,1; 0,5,5,3,1; ...
%Y A059365 See also the triangle in A009766. First 2 diagonals both give A000108, 
               next give A000245, A002057.
%Y A059365 Cf. A009766 A000007 A084938 A000108.
%Y A059365 The three triangles A059365, A106566 and A099039 are the same except 
               for signs and the leading term.
%Y A059365 Essentially the same as A033184.
%Y A059365 The following are all versions of (essentially) the same Catalan triangle: 
               A009766, A030237, A033184, A059365, A099039, A106566, A130020, A047072.
%Y A059365 Diagonals give A000108 A000245 A002057 A000344 A003517 A000588 A003518 
               A003519 A001392, ...
%Y A059365 Sequence in context: A128497 A011434 A147746 this_sequence A099039 A106566 
               A049244
%Y A059365 Adjacent sequences: A059362 A059363 A059364 this_sequence A059366 A059367 
               A059368
%K A059365 nonn,tabl
%O A059365 0,8
%A A059365 N. J. A. Sloane (njas(AT)research.att.com), Jan 28 2001

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