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A173841 Number of permutations of 1..n with no adjacent pair summing to n+1. 3

%I #10 Jul 21 2019 17:20:23

%S 1,1,0,2,8,48,240,1968,13824,140160,1263360,15298560,168422400,

%T 2373073920,30865121280,496199854080,7445355724800,134510244986880,

%U 2287168006717440,45877376537395200,871804170613555200,19225435113632563200,403779880746418176000

%N Number of permutations of 1..n with no adjacent pair summing to n+1.

%C 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]

%F k = 1; a(n,k) = Sum_{j=0..m} (-2)^j*binomial(m,j)*(n-j)! where m = max(0, floor((n-k+1)/2)). [From _Max Alekseyev_, on the Sequence Fans Mailing List]

%K nonn

%O 0,4

%A _R. H. Hardin_, Feb 26 2010

%E More terms from _Alois P. Heinz_, Jan 09 2017

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)