A173842 Number of permutations of 1..n with no adjacent pair summing to n+2.

1, 1, 2, 2, 12, 48, 336, 1968, 17760, 140160, 1543680, 15298560, 199019520, 2373073920, 35611269120, 496199854080, 8437755432960, 134510244986880, 2556188496691200, 45877376537395200, 963558923688345600, 19225435113632563200, 442230750973683302400

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 = 2; 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: A087131 A199240 A349529 * A352526 A131444 A291541

Adjacent sequences: A173839 A173840 A173841 * A173843 A173844 A173845

Keyword

nonn

Author

R. H. Hardin, Feb 26 2010

Extensions

More terms from Alois P. Heinz, Jan 09 2017

Status

approved