A181142 Number of permutations of {1,2,...,2n} , say x(1),x(2), ... , x(2n) , such that x(i) + x(i+1) is not equal to 2n-1 for all i, 1<=i<=2n-1.

2, 12, 336, 17760, 1543680, 199019520, 35611269120, 8437755432960, 2556188496691200, 963558923688345600, 442230750973683302400, 242766600433441859174400, 157060798435284559803187200

Offset

1,1

Links

Table of n, a(n) for n=1..13.

Nathan Reading, Assignments

StackExchange, Can this be simplified?

Formula

a(n) = Sum_{k=0}^{n-1} binomial(n -1,k) (-2)^k (2n - k)!.

Conjecture: D-finite with recurrence (-n+1)*a(n) +2*(2*n-1)*(n^2-n-1)*a(n-1) +4*n^2*(n-2)*a(n-2)=0. - R. J. Mathar, Jan 27 2022

Mathematica

f[n_] := Sum[(-2)^k (2 n - k)! Binomial[n - 1, k], {k, 0, n - 1}]; Array[f, 13] (* Robert G. Wilson v, Oct 16 2010 *)

Prog

(Other) SAS datastep: data _null_; do n = 1 to 7; a = 0; do _n_ = 0 to n-1; a = a + (-2)**_n_ * comb(n-1, _n_)*fact(2*n-_n_); end; output; put "a(" n ")=" a; end; run;

Crossrefs

Sequence in context: A012727 A296622 A325756 * A088229 A060596 A074257

Adjacent sequences: A181139 A181140 A181141 * A181143 A181144 A181145

Keyword

nonn

Author

Arin Chaudhuri (arin.chaudhuri(AT)gmail.com), Oct 06 2010

Extensions

a(8) and onward from Robert G. Wilson v, Oct 16 2010

Status

approved