%I A052609
%S A052609 0,0,4,24,144,960,7200,60480,564480,5806080,65318400,798336000,
%T A052609 10538035200,149448499200,2266635571200,36614882304000,
%U A052609 627683696640000,11381997699072000,217680705994752000
%N A052609 (2*n-2)*n!.
%C A052609 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 (deutsch(AT)duke.poly.edu), 
               Apr 06 2008
%C A052609 a(n)=A138770(n+2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 
               2008
%H A052609 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=554">
               Encyclopedia of Combinatorial Structures 554</a>
%F A052609 E.g.f.: 2*x^2/(-1+x)^2
%F A052609 Recurrence: {a(1)=0, a(0)=0, a(2)=4, (-n^2-n)*a(n)+(n-1)*a(n+1)}
%p A052609 spec := [S,{S=Prod(Z,Sequence(Z),Sequence(Z),Union(Z,Z))},labeled]: seq(combstruct[count](spec,
               size=n), n=0..20);
%Y A052609 Cf. A138770.
%Y A052609 Sequence in context: A121102 A067411 A045915 this_sequence A077613 A072949 
               A104531
%Y A052609 Adjacent sequences: A052606 A052607 A052608 this_sequence A052610 A052611 
               A052612
%K A052609 easy,nonn
%O A052609 0,3
%A A052609 encyclopedia(AT)pommard.inria.fr, Jan 25 2000