|
Search: id:A027363
|
|
|
| A027363 |
|
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. |
|
+0
1
|
|
| 1, 27, 2875, 698005, 305093061, 210480374951, 210776836330775, 289139638632755625, 520764738758073845321, 1192221463356102320754899, 3381929766320534635615064019, 11643962664020516264785825991165
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
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.
|
|
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]
|
|
CROSSREFS
|
Sequence in context: A017427 A050644 A048567 this_sequence A085529 A132659 A104131
Adjacent sequences: A027360 A027361 A027362 this_sequence A027364 A027365 A027366
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
Paolo Dominici (pl.dm(AT)libero.it), Oct 15 1997
|
|
|
Search completed in 0.003 seconds
|
