%I #2 Mar 30 2012 17:34:34
%S 0,1,1,2,2,2,3,3,3,3,4,6,2,6,4,5,10,5,5,10,5,6,15,15,0,15,15,6,7,21,
%T 35,0,0,35,21,7,8,28,70,1,0,1,70,28,8,9,36,126,9,0,0,9,126,36,9,10,45,
%U 210,45,0,0,0,45,210,45,10
%N Triangle T(n,m)= binomial(n,2^m) + binomial(n,2^(n - m)) read by rows.
%C Row sums are {0, 2, 6, 12, 22, 40, 72, 126, 214, 360, 620,...}.
%F T(n,m)=binomial(n, 2^m) + binomial(n, 2^(n - m)) = T(n,n-m).
%e {0},
%e {1, 1},
%e {2, 2, 2},
%e {3, 3, 3, 3},
%e {4, 6, 2, 6, 4},
%e {5, 10, 5, 5, 10, 5},
%e {6, 15, 15, 0, 15, 15, 6},
%e {7, 21, 35, 0, 0, 35, 21, 7},
%e {8, 28, 70, 1, 0, 1, 70, 28, 8},
%e {9, 36, 126, 9, 0, 0, 9, 126, 36, 9},
%e {10, 45, 210, 45, 0, 0, 0, 45, 210, 45, 10}
%t t[n_, m_] = Binomial[n, 2^m] + Binomial[n, 2^(n - m)];
%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%K nonn,tabl
%O 0,4
%A _Roger L. Bagula_, Mar 08 2009
%E Edited by the Associate Editors of the OEIS, Apr 10 2009