A173843 Number of permutations of 1..n with no adjacent pair summing to n+3.

1, 1, 2, 6, 12, 72, 336, 2640, 17760, 175680, 1543680, 18385920, 199019520, 2771112960, 35611269120, 567422392320, 8437755432960, 151385755852800, 2556188496691200, 50989753530777600, 963558923688345600, 21152552961009254400, 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 = 3; 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: A076220 A258213 A178846 * A107763 A166470 A144144

Adjacent sequences: A173840 A173841 A173842 * A173844 A173845 A173846

Keyword

nonn

Author

R. H. Hardin, Feb 26 2010

Extensions

More terms from Alois P. Heinz, Jan 09 2017

Status

approved