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%I #8 Oct 14 2024 08:10:30
%S 7736,34659,138022,511412,1807840,6188910,20713252,68199003,221845712,
%T 715077749,2288733954,7285025030,23085311544,72888488904,229435695984,
%U 720341436677,2256533814344,7054866364855,22017726215966,68606973122472
%N Number of permutations of 1..n+7 with the number moved left exceeding the number moved right by n.
%C Recurrence would also extend to an a(0) if the definition were made to exclude the identity permutation.
%H R. H. Hardin, <a href="/A179574/b179574.txt">Table of n, a(n) for n=1..32</a>
%F Empirical: a(n)=20*a(n-1)-180*a(n-2)+964*a(n-3)-3422*a(n-4)+8484*a(n-5)-15068*a(n-6)+19324*a(n-7)-17769*a(n-8)+11432*a(n-9)-4888*a(n-10)+1248*a(n-11)-144*a(n-12) ; G.f.: -x*(-7736 +120061*x -837322*x^2 +3467912*x^3 -9484876*x^4 +17996064*x^5 -24175460*x^6 +22995433*x^7 -15176808*x^8 +6618712*x^9 -1716576*x^10 +200592*x^11) / ( (-1+3*x)^2*(2*x-1)^4*(x-1)^6 ).
%K nonn
%O 1,1
%A _R. H. Hardin_, g.f. from R. J. Mathar in the Sequence Fans Mailing List, Jul 19 2010