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A129937
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The central binomial numbers Binomial[n,Floor[n/2] minus the SO(n) dimension as an algebraic projective variety dimension.
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0
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1, 1, 0, 0, 0, 5, 14, 42, 90, 207, 407, 858, 1638, 3341, 6330, 12750, 24174, 48467, 92207, 184566, 352506, 705201, 1351825, 2703880, 5200000, 10400275, 20057949, 40116222, 77558354, 155117085
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| Alternative summing form gives the same answer: f[n_] = Binomial[n, Floor[n/2]] - Binomial[n - 1, Floor[(n - 1)/2]] g[n_] = Sum[f[m + 1], {m, 1, n}] + 1 - Sum[m, {m, 1, n}] Table[g[n], {n, 0, 29}] That a(n) of n=3,4,5 are all zero seems important here.
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REFERENCES
| http://mathworld.wolfram.com/SchubertVariety.html
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FORMULA
| a(n) = Binomial[n, Floor[n/2]] - n*(n - 1)/2
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MATHEMATICA
| k[n_] = Binomial[n, Floor[n/2]] - n*(n - 1)/2; Table[k[n], {n, 1, 30}]
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CROSSREFS
| Sequence in context: A122485 A198086 A032249 * A147978 A034549 A180774
Adjacent sequences: A129934 A129935 A129936 * A129938 A129939 A129940
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 09 2007
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