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a(n) = (1-(n-1)/2^n)*(n!)^n.
1

%I #13 Dec 30 2023 13:48:26

%S 2,1,3,162,269568,21772800000,128430157824000000,

%T 78734235726376796160000000,6793969131008738346811156070400000000,

%U 107405833909078014660339510303458240495616000000000,392460917103771065568880570648836410770980864000000000000000000000,407931390497527236736237611020825246476822200409679741237329920000000000000000000000

%N a(n) = (1-(n-1)/2^n)*(n!)^n.

%H Morton Abramson, David Promislow, <a href="https://doi.org/10.1016/0097-3165(78)90012-2">Enumeration of arrays by column rises</a>, J. Combinatorial Theory Ser. A 24 (1978), no. 2, 247--250. MR0469773 (57 #9554).

%t Table[(1-(n-1)/2^n)(n!)^n,{n,0,15}] (* _Harvey P. Dale_, Dec 30 2023 *)

%o (PARI) a(n) = (1-(n-1)/2^n)*(n!)^n; \\ _Michel Marcus_, Feb 27 2018

%Y Cf. A212806.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, May 27 2012