A275801 Number of alternating permutations of the multiset {1,1,2,2,...,n,n}.

1, 0, 1, 4, 53, 936, 25325, 933980, 45504649, 2824517520, 217690037497, 20394614883316, 2282650939846781, 300814135522967736, 46103574973075123877, 8130996533576437261772, 1635028654501420083152785, 371853339350614571322913824, 94969025880924845123887493233

Offset: 0

Author

Max Alekseyev, Aug 09 2016

Keywords

• nonn

Comments

Number of permutations (p(1),...,p(2n)) of {1,1,2,2,...,n,n} satisfying p(1) < p(2) > p(3) < ... < p(2n).

a(n) <= A005799(n) <= A275829(n).

Links

• Max Alekseyev, Table of n, a(n) for n = 0..70
• Wikipedia, Alternating permutation.
• hkju et al., Number of updown sequences of 1,1,2,2,...,n,n, Mathoverflow, 2016.

Crossrefs

Column k=2 of A275784.

Cf. A000111, A001250, A000459, A004075, A005799, A114938, A137729, A137730, A137737, A137749, A275829.