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%I #29 Aug 13 2016 10:21:01
%S 1,0,1,4,53,936,25325,933980,45504649,2824517520,217690037497,
%T 20394614883316,2282650939846781,300814135522967736,
%U 46103574973075123877,8130996533576437261772,1635028654501420083152785,371853339350614571322913824,94969025880924845123887493233
%N Number of alternating permutations of the multiset {1,1,2,2,...,n,n}.
%C Number of permutations (p(1),...,p(2n)) of {1,1,2,2,...,n,n} satisfying p(1) < p(2) > p(3) < ... < p(2n).
%C a(n) <= A005799(n) <= A275829(n).
%H Max Alekseyev, <a href="/A275801/b275801.txt">Table of n, a(n) for n = 0..70</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Alternating_permutation">Alternating permutation</a>.
%H hkju et al., <a href="http://mathoverflow.net/q/247107">Number of updown sequences of 1,1,2,2,...,n,n</a>, Mathoverflow, 2016.
%Y Column k=2 of A275784.
%Y Cf. A000111, A001250, A000459, A004075, A005799, A114938, A137729, A137730, A137737, A137749, A275829.
%K nonn
%O 0,4
%A _Max Alekseyev_, Aug 09 2016
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