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%I
%S 2,2,2,2,6,2,2,11,11,2,2,17,30,17,2,2,24,63,63,24,2,2,32,115,168,115,
%T 32,2,2,41,192,375,375,192,41,2,2,51,301,748,990,748,301,51,2,2,62,
%U 450,1379,2288,2288,1379,450,62,2
%N A symmetrical sequence: t(n,m)=Binomial[n + m - 1, 2*m] + Binomial[n + n - m - 1 - 1, 2*(n - m - 1)].
%C Row sums are:
%C {2, 4, 10, 26, 68, 178, 466, 1220, 3194, 8362,...}
%F (n,m)=Binomial[n + m - 1, 2*m] + Binomial[n + n - m - 1 - 1, 2*(n - m - 1)].
%e {2},
%e {2, 2},
%e {2, 6, 2},
%e {2, 11, 11, 2},
%e {2, 17, 30, 17, 2},
%e {2, 24, 63, 63, 24, 2},
%e {2, 32, 115, 168, 115, 32, 2},
%e {2, 41, 192, 375, 375, 192, 41, 2},
%e {2, 51, 301, 748, 990, 748, 301, 51, 2},
%e {2, 62, 450, 1379, 2288, 2288, 1379, 450, 62, 2}
%t Table[Table[ Binomial[n + m - 1, 2*m] + Binomial[n + n - m - 1 - 1, 2*(n - m - 1)], {m, 0, n - 1}], {n, 1, 10}];
%t Flatten[%]
%K nonn,tabl,uned,changed
%O 0,1
%A _Roger L. Bagula_, Feb 14 2009
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