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%I #3 Mar 30 2012 18:52:05
%S 1,1,-3,-1,2,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,5,5
%N From Bernoulli twin numbers to Catalan numbers arrays.Second part.Consider array from companion of Bernoulli twin numbers A172083/A051717 mixed with A051716/A051717 BCT(n)=1,1,-3/2,-1/2,2/3,-1/3,-1/6,-1/6, with successive differences,named BCT1.a(n) are numerators of BCT(n).Denominators (double A051717)=1,1,2,2,3,3,6,6,30,30,30,30,.
%C a(n) is A176511 (companion) with A176511(2),A176511(3), A176511(4),A176511(5) swapped by pairs.Rows of BCT1: 1) 1,1,-3/2,-1/2,2/3,-1/3,-1/6,-1/6; 2) 0,-5/2,1,7/6,-1,1/6,0,2/15; 3) -5/2,7/2,1/6,-13/6,7/6,-1/6,2/15,-2/15; 4) 6,-10/3,-7/3,10/3,-4/3,3/10,-4/15,4/15; 5) -28/3,1,17/3,-14/3,49/30,-17/30,8/15,-8/15; 6) 31/3,14/3,-31/3,63/10,-11/5,11/10,16/15; 7) -17/3,-15,499/30,-17/2,33/10,-1/30; 8) -28/3,949/30,-377/15; .Now we subtract first part BTC1 and second BCT1.Hence an array with only integers.We consider it from seventh column from right to left.Columns changed into rows give different possibilities for Catalan numbers A000108 or A000108(n+1). Among them,ECT(n) in A176239. Odd triangle is 1, 1,0,-1, 0,1,-1,0,2, 0,0,1,-2,2,0,-5, 0,0,0,1,-3,5,-5,0,14, .
%K uned,sign
%O 0,3
%A _Paul Curtz_, Apr 26 2010
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