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%I A242087 #13 May 23 2014 13:53:48
%S A242087 1,0,6,6,36,88,376,1096,4476,14200,57284,190206,764812,2615268,
%T A242087 10499504,36677626,147110276,522288944
%N A242087 Number of balanced orbitals over an odd number of sectors.
%C A242087 See A241810 and A232500 for the combinatorial definitions.
%F A242087 a(n) = A241810(2*n+1).
%t A242087 np[z_]:=Module[{i,j},For[i=Length[z],i>1&&z[[i-1]]>=z[[i]],i--]; For[j=Length[z],z[[j]]<=z[[i-1]],j--]; Join[Take[z,i-2],{z[[j]]}, Reverse[Drop[ReplacePart[z,z[[i-1]],j],i-1]]]]; o=Table[1,{16}];
%t A242087 Print[1]; Do[p=Join[-Take[o,n],{0},Take[o,n]]; c=0; Do[If[Accumulate[Accumulate[p]][[-1]]==0,c++]; p=np[p],{(2*n+1)!/(2*n!^2)}]; Print[2*c],{n,16}]
%t A242087 (* _Hans Havermann_, May 10 2014 *)
%o A242087 (Sage)
%o A242087 def A242087(n):
%o A242087     if n == 0: return 1
%o A242087     A = 0; T = [0]
%o A242087     for i in (1..n):
%o A242087         T.append(-1); T.append(1)
%o A242087     for p in Permutations(T):
%o A242087         P = 0; S = 0
%o A242087         for k in (0..2*n):
%o A242087             P += p[k]; S += P
%o A242087         if S == 0: A += 1
%o A242087     return A
%o A242087 [A242087(n) for n in (0..10)]
%K A242087 nonn,more
%O A242087 0,3
%A A242087 _Peter Luschny_, May 04 2014
%E A242087 More terms from _Hans Havermann_, May 10 2014
%E A242087 a(17) from _Hans Havermann_, May 23 2014

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