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%I #14 Nov 10 2013 15:43:31
%S 1,1,0,1,1,0,1,2,2,0,1,3,6,4,0,1,4,12,16,8,0,1,5,20,40,40,16,0,1,6,30,
%T 80,120,96,32,0,1,7,42,140,280,336,224,64,0,1,8,56,224,560,896,896,
%U 512,128,0,1,9,72,336,1008,2016,2688,2304,1152,256,0
%N Triangle T(n,k), read by rows, given by (1,0,0,1,0,0,0,0,0,0,0,...) DELTA (0,1,1,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.
%C Mirror image of A198792.
%C Variant of A082137.
%F Sum_ {0<=k<=n} T(n,k) = A124302(n).
%F G.f.:(1-x*(1+2y)+x^2*y)/((1-x)*(1-(1+2y)*x)).
%F T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1) for n>2, T(0,0) = T(1,0) = T(2,0) = T(2,1) = 1, T(1,1) = T(2,2) = 0, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Nov 10 2013
%e Triangle begins :
%e 1
%e 1, 0
%e 1, 1, 0
%e 1, 2, 2, 0
%e 1, 3, 6, 4, 0
%e 1, 4, 12, 16, 8, 0,
%e 1, 5, 20, 40, 40, 16, 0
%Y Cf. A082137, A084938, A198792.
%K easy,nonn,tabl
%O 0,8
%A _Philippe Deléham_, Oct 30 2011
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