A173846 Number of permutations of 1..n with no adjacent pair summing to n+6.

1, 1, 2, 6, 24, 120, 720, 3600, 30240, 221760, 2338560, 22176000, 280143360, 3242695680, 47638886400, 649729382400, 10872058982400, 170530956288000, 3200021920972800, 56707673547571200, 1178953777845043200, 23283629822509056000, 531103116540719923200

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 = 6; 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: A189860 A274795 A174702 * A154654 A189862 A189863

Adjacent sequences: A173843 A173844 A173845 * A173847 A173848 A173849

Keyword

nonn

Author

R. H. Hardin, Feb 26 2010

Extensions

More terms from Alois P. Heinz, Jan 09 2017

Status

approved