A173845 Number of permutations of 1..n with no adjacent pair summing to n+5.

1, 1, 2, 6, 24, 120, 480, 3600, 23040, 221760, 1895040, 22176000, 235791360, 3242695680, 41153495040, 649729382400, 9572600217600, 170530956288000, 2858960008396800, 56707673547571200, 1065538430749900800, 23283629822509056000, 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 = 5; 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: A189569 A174701 A178848 * A258216 A263748 A072856

Adjacent sequences: A173842 A173843 A173844 * A173846 A173847 A173848

Keyword

nonn

Author

R. H. Hardin, Feb 26 2010

Extensions

More terms from Alois P. Heinz, Jan 09 2017

Status

approved