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A176991
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Triangle t(n,m) = binomial(n+m,m) - binomial(n-m,m), 1<=m<=n, read by rows.
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0
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2, 2, 6, 2, 10, 20, 2, 14, 35, 70, 2, 18, 56, 126, 252, 2, 22, 83, 210, 462, 924, 2, 26, 116, 330, 792, 1716, 3432, 2, 30, 155, 494, 1287, 3003, 6435, 12870, 2, 34, 200, 710, 2002, 5005, 11440, 24310, 48620, 2, 38, 251, 986, 3002, 8008, 19448, 43758, 92378, 184756
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OFFSET
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1,1
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COMMENTS
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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,....
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LINKS
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FORMULA
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EXAMPLE
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2;
2, 6;
2, 10, 20;
2, 14, 35, 70;
2, 18, 56, 126, 252;
2, 22, 83, 210, 462, 924;
2, 26, 116, 330, 792, 1716, 3432;
2, 30, 155, 494, 1287, 3003, 6435, 12870;
2, 34, 200, 710, 2002, 5005, 11440, 24310, 48620;
2, 38, 251, 986, 3002, 8008, 19448, 43758, 92378, 184756;
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MATHEMATICA
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t[n_, m_] = Binomial[n + (m - 1), (m - 1)] - Binomial[n - (m - 1), (m - 1)];
Table[Table[t[n, m], {m, 2, n + 1}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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