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%I #14 Jun 13 2021 03:23:50
%S 1,1,2,2,8,8,132,272,1844,7824,219392,879040,9865488,30363264,
%T 1348905760,26759363296,265338415104,1871331759456,24675601835904,
%U 166652846570112,1969110048305664,22090834149738048,2586719545294006272,22961806952814951168,289429435718440962048
%N Number of permutations of [n] such that the product of the first k elements and the product of the last k elements are multiples of k for all k in [n].
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%e a(5) = 8: 12345, 14325, 14352, 21345, 25341, 52341, 54312, 54321.
%Y Cf. A333711, A333892.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Apr 10 2020