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%I #3 Mar 30 2012 17:26:55
%S 1,1,2,6,12,36,86,270,746,2554,8032,29716,103482,409242,1550850,
%T 6508702,26509428,117368404,508962350,2365560998,10842378698,
%U 52685516658,253754085960,1284660919140,6471281910962,34031293950258
%N Number of ways to seat n people around a circular table such that person i is next to person i-1 or i+1 or both.
%F For n>=3, a(n)=2+2*Sum_{k=2..[n/2]} (C(n-k,k) + C(n-k-1,k-1))*A061714(k)
%o (PARI) { a(n) = if(n<3, 1, 2 + 2*sum(k=2,n\2, (binomial(n-k,k)+binomial(n-k-1,k-1)) * ((-1)^k+sum(i=0,k-1,(-1)^(k-1-i)*binomial(k,i+1)*i!*2^i)) ) ) }
%K nonn
%O 1,3
%A _Max Alekseyev_, Jul 03 2006
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