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a(n) = (n-1)*n!*(n-1)!.
0

%I #9 Sep 07 2024 16:02:43

%S 0,2,24,432,11520,432000,21772800,1422489600,117050572800,

%T 11851370496000,1448500838400000,210322321735680000,

%U 35793035117199360000,7057193423941140480000,1596011435875919462400000,410402940653807861760000000,119071573181691454291968000000

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

%C For n > 2, the number of minimum vertex colorings of the n-barbell graph.

%C a(n) is also the number of minimum distinguishing labelings of the (n-1) x (n-1) complete bipartite graph K_n,n. - _Eric W. Weisstein_, Sep 07 2024

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarbellGraph.html">Barbell Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DistinguishingNumber.html">Distinguishing Number</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumVertexColoring.html">Minimum Vertex Coloring</a>.

%t Table[(n - 1) n! (n - 1)!, {n, 20}]

%t Table[(n - 1) n Gamma[n]^2, {n, 20}]

%t Table[2 Binomial[n, 2] Gamma[n]^2, {n, 20}]

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Mar 03 2024