%I A110104
%S A110104 1,4,3760,23504320,567399078400,37518268781593600,
%T A110104 5543744611870143078400,1599334510537656091623424000,
%U A110104 818296434784062385011283591168000
%N A110104 a(n) is the number of coverings of 1...n by cyclic words of length 3n, 
               such that each value from 1 to n appears precisely twice. That is, 
               the union of all the letters in all of the words of a given covering 
               is the multiset {1,1,2,2,...,n,n}. No repeats of words are allowed 
               in a given covering.
%C A110104 P-recursive
%F A110104 Differential equation satisfied by egf: sum a(n)t^3n/(3n!) {F(0) = 1, 
               (-2+4*t^6+16*t^3)*diff(F(t), t)+4*t^4*diff(diff(F(t), t), t)+t^2*(4+12*t^3+t^6)*F(t)} 
               Recurrence: {a(0) = 1, (40320+328752*n+1816668*n^3+1102248*n^5+398034*n^6+1818369*n^4+1063116*n^2+78732*n\
               ^7+6561*n^8)*a(n)+(508608*n+161280+453600*n^3+34992*n^5+2916*n^6+173340*n^4+661104*n^2)*a(n+1)+(12320+199\
               80*n+12096*n^2+3240*n^3+324*n^4)*a(n+2)-2*a(n+3), a(1) = 4, a(2) 
               = 3760}
%e A110104 a(1)=4: {123, 132} {112, 233} {113, 322} {133, 122}
%Y A110104 Cf. A052502, A110105, A110106, A108242.
%Y A110104 Sequence in context: A134908 A114498 A069120 this_sequence A024061 A067482 
               A013830
%Y A110104 Adjacent sequences: A110101 A110102 A110103 this_sequence A110105 A110106 
               A110107
%K A110104 easy,nonn
%O A110104 0,2
%A A110104 Marni Mishna (marni.mishna(AT)inria.fr), Jul 11 2005