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%I #7 Jun 17 2015 04:13:08
%S 1,1,1,1,3,1,1,5,5,1,1,14,16,14,1,1,44,55,55,44,1,1,146,187,196,187,
%T 146,1,1,504,647,686,686,647,504,1,1,1786,2287,2428,2458,2428,2287,
%U 1786,1,1,6449,8232,8731,8863,8863,8731,8232,6449,1,1,23635,30081,31862,32352
%N Triangle T(n,m) = 2+A176697(n)-A176697(m)-A176697(n-m) read along rows 0<=m<=n.
%C Row sums are 1, 2, 5, 12, 46, 200, 864, 3676, 15462, 64552, 268316,...
%F T(n,k) = T(n,n-k).
%e 1;
%e 1, 1;
%e 1, 3, 1;
%e 1, 5, 5, 1;
%e 1, 14, 16, 14, 1;
%e 1, 44, 55, 55, 44, 1;
%e 1, 146, 187, 196, 187, 146, 1;
%e 1, 504, 647, 686, 686, 647, 504, 1;
%e 1, 1786, 2287, 2428, 2458, 2428, 2287, 1786, 1;
%e 1, 6449, 8232, 8731, 8863, 8863, 8731, 8232, 6449, 1;
%e 1, 23635, 30081, 31862, 32352, 32454, 32352, 31862, 30081, 23635, 1;
%p A176700 :=proc(n,k)
%p 2+A176697(n)-A176697(k)-A176697(n-k) ;
%p end proc: # _R. J. Mathar_, Jun 17 2015
%t a[0] := 1; a[1] := 1;a[2]=3
%t a[n_] := a[n] = Table[a[i], {i, 0, n - 1}].Table[a[n - 1 - i], {i, 0, n - 1}];
%t t[n_, m_] := 2 + (-a[m] - a[n - m] + a[n]);
%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]
%Y Cf. A176697.
%K nonn,tabl,easy
%O 0,5
%A _Roger L. Bagula_, Apr 24 2010
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