%I A123149
%S A123149 1,1,0,1,1,0,1,1,1,0,1,2,2,1,0,1,2,3,2,1,0,1,3,5,5,3,1,0,1,3,6,7,6,3,1,
%T A123149 0,1,4,9,13,13,9,4,1,0,1,4,10,16,19,16,10,4,1,0,1,5,14,26,35,35,26,14,
               5,
%U A123149 1,0,1,5,15,30,45,51,45,30,15,5,1,0,1,6,20,45,75,96,96,75,45,20,6,1,0,
               1
%N A123149 Triangle T(n,k), 0<=k<=n, read by rows given by [1, 0, -1, 0, 0, 0, 0, 
               0, ...] DELTA [0, 1, 0, -1, 0, 0, 0, 0, ...] where DELTA is the operator 
               defined in A084938.
%F A123149 T(n,k)=T(n,n-1-k) . Sum_{k, 0<=k<=n}T(n,k)=A038754(n-1), for n>=1 . T(2*n,
               n)=A005773(n) . T(2*n+1,n)=A002426(n) . T(n,k)=T(n-1,k-1)+T(n-1,k)if 
               n even, T(n,k)=T(n-1,k-1)+T(n-2,k)if n odd, T(0,0)=1, T(1,0)=1, T(1,
               1)=0, T(n,k)=0 if k<0 or if k>n.
%e A123149 Triangle begins:
%e A123149 1;
%e A123149 1, 0;
%e A123149 1, 1, 0;
%e A123149 1, 1, 1, 0;
%e A123149 1, 2, 2, 1, 0;
%e A123149 1, 2, 3, 2, 1, 0;
%e A123149 1, 3, 5, 5, 3, 1, 0;
%e A123149 1, 3, 6, 7, 6, 3, 1, 0;
%e A123149 1, 4, 9, 13, 13, 9, 4, 1, 0;
%Y A123149 Cf. A027907.
%Y A123149 Sequence in context: A055892 A104244 A116403 this_sequence A061926 A053188 
               A109389
%Y A123149 Adjacent sequences: A123146 A123147 A123148 this_sequence A123150 A123151 
               A123152
%K A123149 nonn,tabl
%O A123149 0,12
%A A123149 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 05 2006