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\[\frac{\left(\mathsf{lgamma} \left( 2 \cdot n + 1 \right) - \mathsf{lgamma} \left( n + 2 \right)\right) - \mathsf{lgamma} \left( n + 1 \right)}{\log 10}\]
\frac{\left(\mathsf{lgamma} \left( 2 \cdot n + 1 \right) - \mathsf{lgamma} \left( n + 2 \right)\right) - \mathsf{lgamma} \left( n + 1 \right)}{\log 10}
double code(double n) {
	return ((double) (((double) (((double) (((double) lgamma(((double) (((double) (2.0 * n)) + 1.0)))) - ((double) lgamma(((double) (n + 2.0)))))) - ((double) lgamma(((double) (n + 1.0)))))) / ((double) log(10.0))));
}

Reproduce

herbie shell --seed 2020152 
(FPCore (n)
  :name "(/ (- (- (lgamma (+ (* 2 n) 1)) (lgamma (+ n 2))) (lgamma (+ n 1))) (log 10))"
  :precision binary64
  (/ (- (- (lgamma (+ (* 2.0 n) 1.0)) (lgamma (+ n 2.0))) (lgamma (+ n 1.0))) (log 10.0)))