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

0,3

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

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)}.

Maple

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

Prog

(Magma) [0], [(2*n-2)*Factorial(n): n in [1..25]]; // Vincenzo Librandi, Oct 11 2011
(PARI) a(n)=(2*n-2)*n! \\ Charles R Greathouse IV, Nov 20 2011

Crossrefs

Cf. A138770.

Sequence in context: A307526 A067411 A045915 * A077613 A072949 A104531

Adjacent sequences: A052606 A052607 A052608 * A052610 A052611 A052612

Keyword

easy,nonn

Author

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

Status

approved