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A173848
Number of permutations of 1..n with no adjacent pair summing to n + 8.
0
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.
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
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