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%I #21 May 23 2020 23:57:16
%S 1,2,15,116,1165,13974,195643,3130280,56345049,1126900970,24791821351,
%T 595003712412,15470096522725,433162702636286,12994881079088595,
%U 415836194530835024,14138430614048390833,508983502105742069970,19341373080018198658879,773654923200727946355140
%N The number of indirect isometries that are derangements of the (n-1)-dimensional facets of an n-cube.
%C a(n) plays the same role as A000387 plays for the derangement numbers A000166.
%H G. Gordon and E. McMahon, <a href="http://arxiv.org/abs/0906.4253">Moving faces to other places: facet derangements</a>, arXiv:0906.4253 [math.CO], 2009.
%H Gary Gordon and Elizabeth McMahon, <a href="http://www.jstor.org/stable/10.4169/000298910X523353">Moving faces to other places: facet derangements</a>, Amer. Math. Monthly, 117 (2010), 865-88.
%F a(n) = (b(n) + (-1)^(n+1))/2, where b(n) is sequence A000354, i.e., the number of (n-1)-dimensional facet derangements of an n-cube.
%F From _Peter Luschny_, May 09 2017: (Start)
%F a(n) = (-1)^(n+1)*n*hypergeom([1, 1-n], [], 2).
%F a(n) = (2^n*Gamma(n+1,-1/2)/exp(1/2)-(-1)^n)/2. (End)
%F E.g.f.: x*exp(-x) / (1 - 2*x). - _Ilya Gutkovskiy_, May 23 2020
%e For a square, the 2 diagonal reflections are indirect edge derangements. For a 3-cube, the 15 rotary reflections are indirect face derangements.
%p a := n -> (-1)^(n+1)*n*hypergeom([1,1-n],[],2):
%p seq(simplify(a(n)), n=1..20); # _Peter Luschny_, May 09 2017
%t a[n_] := (-1)^(n + 1)*n*HypergeometricPFQ[{1, 1 - n}, {}, 2];
%t Array[a, 20] (* _Jean-François Alcover_, Jul 14 2018, after _Peter Luschny_ *)
%Y Cf. A000354, A000387, A161936.
%K easy,nonn
%O 1,2
%A Elizabeth McMahon, Gary Gordon (mcmahone(AT)lafayette.edu), Jun 29 2009
%E More terms from _Peter Luschny_, May 09 2017
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