A173841 Number of permutations of 1..n with no adjacent pair summing to n+1.

1, 1, 0, 2, 8, 48, 240, 1968, 13824, 140160, 1263360, 15298560, 168422400, 2373073920, 30865121280, 496199854080, 7445355724800, 134510244986880, 2287168006717440, 45877376537395200, 871804170613555200, 19225435113632563200, 403779880746418176000

Offset: 0

Author

R. H. Hardin, Feb 26 2010

Keywords

• nonn
• changed

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]

Crossrefs

Cf. A007060 (bisection), A285850.

Formula

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

a(2n) = A007060(n); a(2n-1) = A285850(n)/(2n). - David Radcliffe, Sep 09 2025

Extensions

More terms from Alois P. Heinz, Jan 09 2017