A173849 - OEIS

%I #8 Jan 09 2017 15:57:14

%S 1,1,2,6,24,120,720,5040,40320,362880,2903040,32659200,333849600,

%T 4470681600,55244851200,855496857600,12362073292800,216999220838400,

%U 3584572069478400,70276861528473600,1305169212624076800,28251875803447296000,582386191297118208000

%N Number of permutations of 1..n with no adjacent pair summing to n + 9.

%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.

%F k = 9; m = max(0, floor((n-k+1)/2)); a(n,k) = Sum_{j=0..m} (-2)^j * binomial(m,j)*(n-j)!.

%K nonn

%O 0,3

%A _R. H. Hardin_, Feb 26 2010

%E Comment proved by William Keith, formula from _Max Alekseyev_, on the Sequence Fans Mailing List

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