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A027363
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Generalizing the 27 lines on a cubic surface: number of lines on the generic hypersurface of degree 2n-1 in complex projective (n+1)-space.
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1, 27, 2875, 698005, 305093061, 210480374951, 210776836330775, 289139638632755625, 520764738758073845321, 1192221463356102320754899, 3381929766320534635615064019, 11643962664020516264785825991165
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Daniel B. Grunberg and Pieter Moree, with an Appendix by Don Zagier, Sequences of enumerative geometry: congruences and asymptotics, arXiv math.NT/0610286.
Van der Waerden, see one of his `Zur algebraischen Geometrie' papers.
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FORMULA
| Let b(n, i)=i/(n-i+1) and g(n, k)=s[ k ](b(n, 1), b(n, 2), ..., b(n, n)), where s[ k ] is the k-th elementary symmetric function; a(n) = (2n-1)^2 * (2n-2)! * [ g(2n-2, n-1) - g(2n-2, n) ].
a_n is the coefficient of x^{n-1} in the polynomial (1-X) prod_{j=0...2n-3}(2n-3-j+jX). [Van der Waerden]
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MATHEMATICA
| a[n_] := Coefficient[ (1-x)*Product[ 2n-1-j+j*x, {j, 0, 2n-1}], x, n]; Table[a[n], {n, 1, 12}] (* From Jean-François Alcover, Jan 23 2012, from second formula *)
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CROSSREFS
| Sequence in context: A017427 A050644 A048567 * A085529 A132659 A104131
Adjacent sequences: A027360 A027361 A027362 * A027364 A027365 A027366
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KEYWORD
| nonn,nice
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AUTHOR
| Paolo Dominici (pl.dm(AT)libero.it), Oct 15 1997
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