A173848 Number of permutations of 1..n with no adjacent pair summing to n + 8.

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 282240, 2903040, 26853120, 333849600, 3802982400, 55244851200, 745007155200, 12362073292800, 192275074252800, 3584572069478400, 63107717389516800, 1305169212624076800, 25641537378199142400, 582386191297118208000

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.

Links

Table of n, a(n) for n=0..22.

Formula

k = 8; m = max(0, floor((n-k+1)/2)); a(n,k) = Sum_{j=0..m} (-2)^j * binomial(m,j)*(n-j)!.

Crossrefs

Sequence in context: A364428 A273695 A177279 * A154656 A179354 A179360

Adjacent sequences: A173845 A173846 A173847 * A173849 A173850 A173851

Keyword

nonn

Author

R. H. Hardin, Feb 26 2010

Extensions

Comment proved by William Keith, formula from Max Alekseyev, on the Sequence Fans Mailing List

More terms from Alois P. Heinz, Jan 09 2017

Status

approved