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Didier Guillet, <a href="/A056040/a056040.pdf">On swinging factorials and the lonely runner conjecture</a> (Text in French).
a(n) = n!/floor(n/2)!^2. [Essentially the original name.]
a(n) = n!/floor(n/2)!^2.
a(n) is the number of vertices of the polytope resulting from the intersection of a an n-hypercube with the hyperplane perpendicular to and bisecting one of its long diagonals at its midpoint. - Didier Guillet, Jun 11 2018 [Edited by Peter Munn, Dec 06 2022]
a(n) is the number of vertices of the polytope resulting of from the intersection of a n-hypercube with the hyperplane perpendicular to one of its diagonals at its diagonalmidpoint. - Didier Guillet, Jun 11 2018 [Edited by _Peter Munn_, Dec 06 2022]
Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/Orbitals">Orbitals</a>.
Didier Guillet, <a href="/A056040/a056040.pdf">On swinging factorials and the lonely runner conjecture</a>.
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Sum_{n>=0} 1/a(n) = 4/3 + 8*Pi/(9*sqrt(3)). - Alexander R. Povolotsky, Aug 18 2012
Sum_{n>=0} 1/a(n) = 4/3 + 8*Pi/(9*sqrt(3)). - Alexander R. Povolotsky, Aug 18 2012
From _Sum_{n>=0} (-1)^n/a(n) = 4/3 - 4*Pi/(9*sqrt(3)). - _Amiram Eldar_, Mar 10 2022: (Start)
Sum_{n>=0} 1/a(n) = 8*Pi/(9*sqrt(3)) + 4/3.
Sum_{n>=0} (-1)^n/a(n) = 4/3 - 4*Pi/(9*sqrt(3)). (End)
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