= Solution
Write $L(N)=(N+a)\ln N-N+b$. The two data points give the linear equations $a\ln10+b=15.104413-10\ln10+10$ and $a\ln50+b=148.477767-50\ln50+50$. Subtraction and back-substitution give
$$
a\simeq0.4958592390,\qquad b\simeq0.9368039780,
$$
or \b[$a=0.4959$, $b=0.9368$ to four significant figures]. The six-decimal-place value $148.477767$ here is the one printed in the original PDF. Retain guard digits for the estimates below. The fitted coefficients are close to the <Stirling's formula> values $1/2$ and $\tfrac12\ln(2\pi)$ but need not equal them because the fit absorbs finite-$N$ corrections.
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