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A176991 Triangle t(n,m) = binomial(n+m,m) - binomial(n-m,m), 1<=m<=n, read by rows.

%I A176991 #8 Mar 12 2014 16:37:17
%S A176991 2,2,6,2,10,20,2,14,35,70,2,18,56,126,252,2,22,83,210,462,924,2,26,
%T A176991 116,330,792,1716,3432,2,30,155,494,1287,3003,6435,12870,2,34,200,710,
%U A176991 2002,5005,11440,24310,48620,2,38,251,986,3002,8008,19448,43758,92378,184756
%N A176991 Triangle t(n,m) = binomial(n+m,m) - binomial(n-m,m), 1<=m<=n, read by rows.
%C A176991 Row sums are binomial(2n+1,n+1)-1-A000071(n+1) = A001700(n)-A000045(n+1) = 2, 8, 32, 121, 454, 1703, 6414, 24276, 92323, 352627,....
%F A176991 t(n,m) = A046899(n,m) - A011973(n,m), 0<=m<=n/2.
%e A176991 2;
%e A176991 2, 6;
%e A176991 2, 10, 20;
%e A176991 2, 14, 35, 70;
%e A176991 2, 18, 56, 126, 252;
%e A176991 2, 22, 83, 210, 462, 924;
%e A176991 2, 26, 116, 330, 792, 1716, 3432;
%e A176991 2, 30, 155, 494, 1287, 3003, 6435, 12870;
%e A176991 2, 34, 200, 710, 2002, 5005, 11440, 24310, 48620;
%e A176991 2, 38, 251, 986, 3002, 8008, 19448, 43758, 92378, 184756;
%t A176991 t[n_, m_] = Binomial[n + (m - 1), (m - 1)] - Binomial[n - (m - 1), (m - 1)];
%t A176991 Table[Table[t[n, m], {m, 2, n + 1}], {n, 1, 10}];
%t A176991 Flatten[%]
%Y A176991 Cf. A046899, A178300, A001791
%K A176991 nonn,tabl
%O A176991 1,1
%A A176991 _Roger L. Bagula_, Dec 08 2010