Search: id:A133607
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%I A133607
%S A133607 1,0,1,0,1,1,0,1,1,1,0,1,1,2,1,0,1,1,3,2,1,0,1,1,4,3,3,1,0,1,1,5,4,6,3,
%T A133607 1,0,1,1,6,5,10,6,4,1,0,1,1,7,6,15,10,10,4,1,0,1,1,8,7,21,15,20,10,5,1,
%U A133607 0,1,1,9,8,28,21,35,20,15,5,1
%V A133607 1,0,1,0,1,-1,0,1,-1,-1,0,1,-1,-2,1,0,1,-1,-3,2,1,0,1,-1,-4,3,3,-1,0,1,
               -1,-5,4,6,-3,-1,
%W A133607 0,1,-1,-6,5,10,-6,-4,1,0,1,-1,-7,6,15,-10,-10,4,1,0,1,-1,-8,7,21,-15,
               -20,10,5,-1,0,1,
%X A133607 -1,-9,8,28,-21,-35,20,15,-5,-1
%N A133607 Triangle T(n,k), 0<=k<=n, read by rows given by [0, 1, 0, 0, 0, 0, 0, 
               0, 0, ...] DELTA [1, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA 
               is the operator defined in A084938 .
%C A133607 Another version of A108299 ; unsigned version in A103631 (T(n,k)=A103631(n,
               k)*A057077(k)).
%F A133607 Sum_{k, 0<=k<=n}T(n,k)*x^(n-k)= A057077(n), A010892(n), A000012(n), A001519(n), 
               A001835(n), A004253(n), A001653(n), A049685(n-1), A070997(n-1), A070998(n-1), 
               A072256(n), A078922(n), A077417(n-1), A085260(n), A001570(n-1) for 
               x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 respectively 
               .
%F A133607 Sum_{k, 0<=k<=n}T(n,k)*x^k = A000007(n), A010892(n), A133631(n), A133665(n), 
               A133666(n), A133667(n), A133668(n), A133669(n), A133671(n), A133672(n) 
               for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 respectively .
%e A133607 Triangle begins:
%e A133607 1;
%e A133607 0, 1;
%e A133607 0, 1, -1;
%e A133607 0, 1, -1, -1;
%e A133607 0, 1, -1, -2, 1;
%e A133607 0, 1, -1, -3, 2, 1;
%e A133607 0, 1, -1, -4, 3, 3, -1;
%e A133607 0, 1, -1, -5, 4, 6, -3, -1;
%e A133607 0, 1, -1, -6, 5, 10, -6, -4, 1;
%e A133607 0, 1, -1, -7, 6, 15, -10, -10, 4, 1;
%e A133607 0, 1, -1, -8, 7, 21, -15, -20, 10, 5, -1;
%e A133607 0, 1, -1, -9, 8, 28, -21, -35, 20, 15, -5, -1;
%e A133607 0, 1, -1, -10, 9, 36, -28, -56, 35, 35, -15, -6, 1 ;...
%e A133607 Triangle A103631 begins:
%e A133607 1;
%e A133607 0, 1;
%e A133607 0, 1, 1;
%e A133607 0, 1, 1, 1;
%e A133607 0, 1, 1, 2, 1;
%e A133607 0, 1, 1, 3, 2, 1;
%e A133607 0, 1, 1, 4, 3, 3, 1;
%e A133607 0, 1, 1, 5, 4, 6, 3, 1;
%e A133607 0, 1, 1, 6, 5, 10, 6, 4, 1;
%e A133607 0, 1, 1, 7, 6, 15, 10, 10, 4, 1;
%e A133607 0, 1, 1, 8, 7, 21, 15, 20, 10, 5, 1;
%e A133607 0, 1, 1, 9, 8, 28, 21, 35, 20, 15, 5, 1;
%e A133607 0, 1, 1, 10, 9, 36, 28, 56, 35, 35, 15, 6, 1 ;...
%e A133607 Triangle A108299 begins:
%e A133607 1;
%e A133607 1, -1;
%e A133607 1, -1, -1;
%e A133607 1, -1, -2, 1;
%e A133607 1, -1, -3, 2, 1;
%e A133607 1, -1, -4, 3, 3, -1;
%e A133607 1, -1, -5, 4, 6, -3, -1;
%e A133607 1, -1, -6, 5, 10, -6, -4, 1;
%e A133607 1, -1, -7, 6, 15, -10, -10, 4, 1;
%e A133607 1, -1, -8, 7, 21, -15, -20, 10, 5, -1;
%e A133607 1, -1, -9, 8, 28, -21, -35, 20, 15, -5, -1;
%e A133607 1, -1, -10, 9, 36, -28, -56, 35, 35, -15, -6, 1 ; ...
%Y A133607 Sequence in context: A080934 A137560 A131255 this_sequence A103631 A083856 
               A081718
%Y A133607 Adjacent sequences: A133604 A133605 A133606 this_sequence A133608 A133609 
               A133610
%K A133607 sign,tabl
%O A133607 0,14
%A A133607 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 27 2007

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