cp's OEIS Frontend

A161936 The number of direct isometries that are derangements of the (n-1)-dimensional facets of an n-cube.

%I A161936 #17 Jul 14 2018 15:36:43
%S A161936 0,3,14,117,1164,13975,195642,3130281,56345048,1126900971,24791821350,
%T A161936 595003712413,15470096522724,433162702636287,12994881079088594,
%U A161936 415836194530835025,14138430614048390832,508983502105742069971,19341373080018198658878,773654923200727946355141
%N A161936 The number of direct isometries that are derangements of the (n-1)-dimensional facets of an n-cube.
%C A161936 a(n) plays the same role as A003221 plays for the derangement numbers A000166.
%H A161936 Gary Gordon, Elizabeth McMahon, <a href="http://arxiv.org/abs/0906.4253">Moving faces to other places: Facet derangements</a>, arXiv:0906.4253 [math.CO], 2009.
%H A161936 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 A161936 a(n) = (b(n) + (-1)^n)/2, where b(n) is sequence A000354, i.e., the number of (n-1)-dimensional facet derangements of an n-cube.
%F A161936 From _Peter Luschny_, May 09 2017: (Start)
%F A161936 a(n) = (-1)^n*(1-n*hypergeom([1,1-n],[],2)).
%F A161936 a(n) = (2^n*Gamma(n+1,-1/2)/exp(1/2)+(-1)^n)/2. (End)
%e A161936 For a square, the 3 rotations are direct edge derangements. For a 3-cube, the 6 edge-centered rotations and the 8 vertex-centered rotations are direct face derangements.
%p A161936 A161936 := n -> (2^n*GAMMA(n+1,-1/2)/exp(1/2)+(-1)^n)/2:
%p A161936 seq(A161936(n), n=1..20); # _Peter Luschny_, May 09 2017
%t A161936 a[n_] := (-1)^n*(1 - n*HypergeometricPFQ[{1, 1 - n}, {}, 2]);
%t A161936 Array[a, 20] (* _Jean-François Alcover_, Jul 14 2018, after _Peter Luschny_ *)
%Y A161936 Cf. A000354, A161937.
%K A161936 easy,nonn
%O A161936 1,2
%A A161936 Elizabeth McMahon, Gary Gordon (mcmahone(AT)lafayette.edu), Jun 29 2009
%E A161936 More terms from _Peter Luschny_, May 09 2017