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%I #14 Nov 10 2013 15:43:46
%S 1,0,1,0,1,1,0,2,2,1,0,4,6,3,1,0,8,16,12,4,1,0,16,40,40,20,5,1,0,32,
%T 96,120,80,30,6,1,0,64,224,336,280,140,42,7,1,0,128,512,896,896,560,
%U 224,56,8,1,0,256,1152,2304,2688,2016,1008,336,72,9,1
%N Triangle T(n,k), read by rows, given by (0,1,1,0,0,0,0,0,0,0,...) DELTA (1,0,0,1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.
%C Row sums are A124302.
%C Variant of A119468.
%F T(n,k) = A097805(n,k)*A011782(n-k).
%F Sum_{0<=k<=n} T(n,k)*2^k = A063376(n-1).
%F G.f.: (1-(y+2)*x+y*x^2)/((1-x*y)*(1-x*(y+2))).
%F T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - 2*T(n-2,k-1) - T(n-2,k-2) for n>2, T(0,0) = T(1,1) = T(2,2) = T(2,1) = 1, T(1,0) = T(2,0) = 0, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Nov 10 2013
%e Triangle begins :
%e 1
%e 0, 1
%e 0, 1, 1
%e 0, 2, 2, 1
%e 0, 4, 6, 3, 1
%e 0, 8, 16, 12, 4, 1
%e 0, 16, 40, 40, 20, 5, 1
%Y Columns include A000007, A011782, A057711, A080929, A082138, A080951, A082139, A082140, A082141, A000012, A001477, A002378.
%K easy,nonn,tabl
%O 0,8
%A _Philippe Deléham_, Oct 30 2011
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