Big round meeting table !

A factory has \(2^n\) workers . Every monday there is ameeting held and all of them sit on a big circular table. All the workers are divided into \(a_1\) type groups each of 2 workers who should sit near each other . they are again divided into \(a_2\) type groups each consisting of 2 \(a_1\) type groups which should sit adjacent to each other . this is continued to form \(a_3\) , \(a_4\) ... type groups .

Find \(2^{n+1}\)-(no of ways the workers can sit on the table)

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