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Let M_n be the n X n matrix with M_n(i,j)=1/(i+j+3); then a(n)=1/det(M_n).
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%I #5 Mar 30 2012 18:38:57

%S 5,1260,8890560,1408264704000,4485780768268800000,

%T 269685408935166352128000000,294004853789028834558485643264000000,

%U 5657409727323500620299434201290024943616000000

%N Let M_n be the n X n matrix with M_n(i,j)=1/(i+j+3); then a(n)=1/det(M_n).

%o (PARI) for(n=1,10,print1(1/matdet(matrix(n,n,i,j,1/(i+j+3))),","))

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Apr 21 2002