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MATHEMATICA
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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}];
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}]
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