A173844 Number of permutations of 1..n with no adjacent pair summing to n+4.

1, 1, 2, 6, 24, 72, 480, 2640, 23040, 175680, 1895040, 18385920, 235791360, 2771112960, 41153495040, 567422392320, 9572600217600, 151385755852800, 2858960008396800, 50989753530777600, 1065538430749900800, 21152552961009254400, 484535856895701811200

Offset

0,3

Comments

If a(n,k) is the number of permutations of 1..n with no adjacent pair summing to n+k, then a(n,k) = a(n,k+1) for n+k even. [proved by William Keith]

Links

Table of n, a(n) for n=0..22.

Formula

k = 4; a(n,k) = Sum_{j=0..m} (-2)^j*binomial(m,j)*(n-j)! where m = max(0, floor((n-k+1)/2)). [Max Alekseyev, on the Sequence Fans Mailing List]

Crossrefs

Sequence in context: A174700 A216158 A178847 * A107761 A147943 A147934

Adjacent sequences: A173841 A173842 A173843 * A173845 A173846 A173847

Keyword

nonn

Author

R. H. Hardin, Feb 26 2010

Extensions

More terms from Alois P. Heinz, Jan 09 2017

Status

approved