Latin square

A Latin square is an n × n matrix of n distinct symbols, where each row and column contains exactly one of each symbol.Wolfram MathWorld, Latin Square
The number of size-n Latin squares is a rapidly growing function, although not terribly impressive compared to other googological functions:
\begin{eqnarray*}
L(1) &=& 1 \\
L(2) &=& 2 \\
L(3) &=& 12 \\
L(4) &=& 576 \\
L(5) &=& 161,280 \\
L(6) &=& 812,851,200 \\
L(7) &=& 61,479,419,904,000
\end{eqnarray*}
No simple formula is yet known for the function \(L(n)\). It is upper-bounded by the function \(n \mapsto (n!)^n\), since each of the \(n\) rows has an arrangement of \(n\) distinct symbols.
=== Sources ===
Category:Exponential growth rate
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