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A359006
Euler characteristics of some Calabi-Yau n-folds.
0
2, 0, 24, -296, 5910, -147624, 4482044, -160180656, 6588215370, -306553312880, 15921704570112, -913109351334168, 57312158437875614, -3907821040411155672, 287639624919939481380, -22731972554599539494624, 1919809166125424793288978, -172552913868209944831000416
OFFSET
1,1
COMMENTS
These numbers are Euler characteristics of Calabi-Yau subvarieties in some weighted projective spaces. See formula B.8 in Bourjaily et alii.
a(n) is divisible by n.
LINKS
Jacob L. Bourjaily, Andrew J. McLeod, Cristian Vergu, Matthias Volk, Matt von Hippel, and Matthias Wilhelm, Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space, arXiv:1910.01534 [hep-th], 2019-2020.
FORMULA
a(n) = (1-(1-2*n)^n+2*n^2)/(2*n).
PROG
(Sage) [(1-(1-2*n)**n+2*n**2)/n/2 for n in range(1, 18)]
CROSSREFS
Sequence in context: A375609 A308506 A255162 * A097563 A360643 A158045
KEYWORD
sign,easy
AUTHOR
F. Chapoton, Dec 10 2022
STATUS
approved