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

0,4

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 = 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]

Crossrefs

Sequence in context: A228288 A356346 A292277 * A004141 A009693 A192251

Adjacent sequences: A173838 A173839 A173840 * A173842 A173843 A173844

Keyword

nonn

Author

R. H. Hardin, Feb 26 2010

Extensions

More terms from Alois P. Heinz, Jan 09 2017

Status

approved