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%I #3 Mar 30 2012 18:59:15
%S 1,0,1,0,-1,1,0,1,-2,1,0,-1,3,-3,1,0,1,-4,6,-4,1,0,-1,5,-9,10,-5,1,0,
%T 1,-6,12,-16,15,-6,1,0,-1,7,-15,19,-25,21,-7,1,0,1,-8,18,-16,20,-36,
%U 28,-8,1,0,-1,9,-21,4,24,6,-49,36,-9,1
%N Number triangle T(n,k)=sum{i=0..n, (-1)^(n-i)*C(n,i)*sum{j=0..i-k, C(k,3j)*C(i-k,3j)}}.
%C Row sums have g.f. (1+x)/(1-x)^6. Multiply by Pascal's triangle A007318 to get A119335.
%F Column k has g.f. (x/(1+x))^k*sum{j=0..k, C(k,3j)x^(3j)}
%e Triangle begins
%e 1,
%e 0, 1,
%e 0, -1, 1,
%e 0, 1, -2, 1,
%e 0, -1, 3, -3, 1,
%e 0, 1, -4, 6, -4, 1,
%e 0, -1, 5, -9, 10, -5, 1,
%e 0, 1, -6, 12, -16, 15, -6, 1,
%e 0, -1, 7, -15, 19, -25, 21, -7, 1,
%e 0, 1, -8, 18, -16, 20, -36, 28, -8, 1,
%e 0, -1, 9, -21, 4, 24, 6, -49, 36, -9, 1
%K easy,sign,tabl
%O 0,9
%A _Paul Barry_, May 14 2006
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