%I A119337
%S A119337 1,0,1,0,1,1,0,1,2,1,0,1,3,3,1,0,1,4,6,4,1,0,1,5,9,10,5,1,0,1,6,12,16,
%T A119337 15,6,1,0,1,7,15,19,25,21,7,1,0,1,8,18,16,20,36,28,8,1,0,1,9,21,4,24,6,
%U A119337 49,36,9,1
%V A119337 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,-5,1,0,1,
               -6,12,-16,15,-6,
%W A119337 1,0,-1,7,-15,19,-25,21,-7,1,0,1,-8,18,-16,20,-36,28,-8,1,0,-1,9,-21,4,
               24,6,-49,36,-9,
%X A119337 1
%N A119337 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 A119337 Row sums have g.f. (1+x)/(1-x)^6. Multiply by Pascal's triangle A007318 
               to get A119335.
%F A119337 Column k has g.f. (x/(1+x))^k*sum{j=0..k, C(k,3j)x^(3j)}
%e A119337 Triangle begins
%e A119337 1,
%e A119337 0, 1,
%e A119337 0, -1, 1,
%e A119337 0, 1, -2, 1,
%e A119337 0, -1, 3, -3, 1,
%e A119337 0, 1, -4, 6, -4, 1,
%e A119337 0, -1, 5, -9, 10, -5, 1,
%e A119337 0, 1, -6, 12, -16, 15, -6, 1,
%e A119337 0, -1, 7, -15, 19, -25, 21, -7, 1,
%e A119337 0, 1, -8, 18, -16, 20, -36, 28, -8, 1,
%e A119337 0, -1, 9, -21, 4, 24, 6, -49, 36, -9, 1
%Y A119337 Sequence in context: A121480 A082601 A077593 this_sequence A110555 A071919 
               A097805
%Y A119337 Adjacent sequences: A119334 A119335 A119336 this_sequence A119338 A119339 
               A119340
%K A119337 easy,sign,tabl
%O A119337 0,9
%A A119337 Paul Barry (pbarry(AT)wit.ie), May 14 2006