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A173842 Number of permutations of 1..n with no adjacent pair summing to n+2. 0
1, 1, 2, 2, 12, 48, 336, 1968, 17760, 140160, 1543680, 15298560, 199019520, 2373073920, 35611269120, 496199854080, 8437755432960, 134510244986880, 2556188496691200, 45877376537395200, 963558923688345600, 19225435113632563200, 442230750973683302400 (list; graph; refs; listen; history; text; internal format)
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 = 2; 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: A237275 A087131 A199240 * A131444 A291541 A180072

Adjacent sequences:  A173839 A173840 A173841 * A173843 A173844 A173845

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 26 2010

EXTENSIONS

More terms from Alois P. Heinz, Jan 09 2017

STATUS

approved

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Last modified September 29 12:15 EDT 2020. Contains 337431 sequences. (Running on oeis4.)