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%I #3 Mar 30 2012 18:59:15
%S 1,0,1,0,-1,1,0,1,-2,1,0,-1,5,-3,1,0,1,-8,12,-4,1,0,-1,11,-28,22,-5,1,
%T 0,1,-14,51,-68,35,-6,1,0,-1,17,-81,159,-135,51,-7,1,0,1,-20,118,-312,
%U 390,-236,70,-8,1,0,-1,23,-162,544,-926,816,-378,92,-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,2j)*C(i-k,2j)*2^j}}.
%C Row sums are A119332. Multiply by Pascal's triangle A007318 to get A119329.
%F Column k has g.f. (x/(1+x))^k*sum{j=0..k, C(k,2j)*2^j*x^(2j)}
%e Triangle begins
%e 1,
%e 0, 1,
%e 0, -1, 1,
%e 0, 1, -2, 1,
%e 0, -1, 5, -3, 1,
%e 0, 1, -8, 12, -4, 1,
%e 0, -1, 11, -28, 22, -5, 1,
%e 0, 1, -14, 51, -68, 35, -6, 1,
%e 0, -1, 17, -81, 159, -135, 51, -7, 1,
%e 0, 1, -20, 118, -312, 390, -236, 70, -8, 1,
%e 0, -1, 23, -162, 544, -926, 816, -378, 92, -9, 1
%K easy,sign,tabl
%O 0,9
%A _Paul Barry_, May 14 2006
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