A052609 a(n) = (2*n - 2)*n!.

0, 0, 4, 24, 144, 960, 7200, 60480, 564480, 5806080, 65318400, 798336000, 10538035200, 149448499200, 2266635571200, 36614882304000, 627683696640000, 11381997699072000, 217680705994752000

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

Number of permutations of {1,2,...,n+2} such that there are exactly two entries between the entries 1 and 2. Example: a(2)=4 because we have 1342, 1432, 2341 and 2431. - Emeric Deutsch, Apr 06 2008

a(n) = A138770(n+2). - Emeric Deutsch, Apr 06 2008

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 554

Crossrefs

Cf. A138770.

Programs

Magma

[0] cat [(2*n-2)*Factorial(n): n in [1..25]]; // Vincenzo Librandi, Oct 11 2011

Maple

spec := [S,{S=Prod(Z,Sequence(Z),Sequence(Z),Union(Z,Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

PARI

a(n)=(2*n-2)*n! \\ Charles R Greathouse IV, Nov 20 2011

Formula

E.g.f.: 2*x^2/(-1+x)^2.

Recurrence: {a(1)=0, a(0)=0, a(2)=4, (-n^2-n)*a(n)+(n-1)*a(n+1)}.