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A179564
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Number of permutations of 1..n with the number moved left exceeding the number moved right by 3.
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1
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0, 0, 0, 0, 1, 6, 134, 960, 16615, 138022, 2425600, 23279224, 444500577, 4880181294, 102914967458, 1277238809792, 29767443364523, 412889949481670, 10588965173821348, 162515224089696984
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