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%I #11 Aug 08 2015 21:32:51
%S 1,1,1,2,2,1,3,3,3,1,5,5,5,4,1,8,8,8,8,5,1,13,13,13,13,12,6,1,21,21,
%T 21,21,21,17,7,1,34,34,34,34,34,33,23,8,1,55,55,55,55,55,55,50,30,9,1,
%U 89,89,89,89,89,89,88,73,38
%N Triangle generated as the matrix product of A026729 and A000012 (triangular views), read by rows.
%C If the triangular factors A026729 and A000012 are commuted in the product, A004070 results.
%C Riordan array (1/(1-x-x^2), x*(1+x)). - _Philippe Deléham_, Mar 06 2013
%F T(n,k) = sum_{j=k..n} binomial(j,n-j). - _R. J. Mathar_, Oct 30 2011
%F T(n,0) = T(n-1,0) + T(n-2,0), T(n,k) = T(n-1,k-1) + T(n-2,k-1) for k>0. - _Philippe Deléham_, Mar 06 2013
%F T(2*n,n) = A000045(2n+1) = A001519(n+1) = A122367(n). - _Philippe Deléham_, Mar 06 2013
%e First few rows of the triangle are
%e 1;
%e 1, 1;
%e 2, 2, 1;
%e 3, 3, 3, 1;
%e 5, 5, 5, 4, 1;
%e 8, 8, 8, 8, 5, 1;
%e 13, 13, 13, 13, 12, 6, 1;
%e 21, 21, 21, 21, 21, 17, 7, 1;
%e ...
%e Production array begins
%e 1, 1
%e 1, 1, 1
%e -1, -1, 1, 1
%e 2, 2, -1, 1, 1
%e -5, -5, 2, -1, 1, 1
%e 14, 14, -5, 2, -1, 1, 1
%e -42, -42, 14, -5, 2, -1, 1, 1
%e 132, 132, -42, 14, -5, 2, -1, 1, 1
%e -429, -429, 132, -42, 14, -5, 2, -1, 1, 1
%e ... which is based on A000108 or A168491. - _Philippe Deléham_, Mar 06 2013
%p A104726 := proc(n,k)
%p add( binomial(j,n-j),j=k..n) ;
%p end proc:
%p seq(seq(A104726(n,k),k=0..n),n=0..10) ; # _R. J. Mathar_, Oct 30 2011
%Y Cf. A001629 (row sums), A026729, A004070, A000071.
%K nonn,easy,tabl
%O 0,4
%A _Gary W. Adamson_, Mar 20 2005
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