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A173849
Number of permutations of 1..n with no adjacent pair summing to n + 9.
0
1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 2903040, 32659200, 333849600, 4470681600, 55244851200, 855496857600, 12362073292800, 216999220838400, 3584572069478400, 70276861528473600, 1305169212624076800, 28251875803447296000, 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 = 9; 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: A276843 A273696 A177280 * A154657 A179361 A179368
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