Ordered Partition Of A Set

A₁, A₂, A₃, ..., A_n

{1, 2} {3, 4} {5}

{1, 2} {4, 3} {5}

{3, 4} {1, 2} {5}.

$T\_n=\backslash sum\_\{i=0\}^\{n-1\}\; \{n\; \backslash choose\; i\}\; T\_i.$

$\backslash sum\_n\; \{T\_n\; \backslash over\; n!\}\; x^n\; =\; \{1\; \backslash over\; 2-e^x\}.$

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