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 A173841 Number of permutations of 1..n with no adjacent pair summing to n+1. 3
 1, 1, 0, 2, 8, 48, 240, 1968, 13824, 140160, 1263360, 15298560, 168422400, 2373073920, 30865121280, 496199854080, 7445355724800, 134510244986880, 2287168006717440, 45877376537395200, 871804170613555200, 19225435113632563200, 403779880746418176000 (list; graph; refs; listen; history; text; internal format)
 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. LINKS FORMULA k = 1; m = \max (0,floor((n-k+1)/2)); a(n,k) = \sum_{j=0}^m (-2)^j \binom{m}{j} (n-j)! CROSSREFS Sequence in context: A193944 A058928 A228288 * A004141 A009693 A192251 Adjacent sequences:  A173838 A173839 A173840 * A173842 A173843 A173844 KEYWORD nonn AUTHOR R. H. Hardin Feb 26 2010, comment proved by William Keith, formula from Max Alekseyev, on the Sequence Fans Mailing List EXTENSIONS More terms from Alois P. Heinz, Jan 09 2017 STATUS approved

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