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%I #8 Sep 08 2013 02:57:13
%S 0,8,900,359424,370828800,820150272000,3435918974208000,
%T 24957654229057536000,294060698786444083200000,
%U 5334667831784096818790400000,42889554205720574193041408000000
%N Number of indecomposable 3-D arrays of 0's and 1's with plane sums 2.
%D P. J. Cameron and T. W. Mueller, Decomposable functors and the exponential principle, II, in preparation
%H P. J. Cameron and T. W. Mueller, <a href="http://arxiv.org/abs/0911.3760v2">Decomposable functors and the exponential principle, II</a>, arXiv:0911.3760 [math.CO]
%F a(1)=0, a(n) = (n!)^2*b(n)/2^n for n>1, where b(0)=1 and sum (n-1 choose k-1)*((2n-2k-1)!!)^2*b(k) = ((2n-1)!!)^2.
%e a(2)=8: six pairs of opposite edges and two inscribed tetrahedra.
%Y Cf. A010796 (2-D case), A112579, A112580.
%K nonn,easy
%O 1,2
%A _Peter J. Cameron_, Sep 14 2005
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