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A104726 Triangle generated as the matrix product of A026729 and A000012 (triangular views), read by rows.

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