In "Kodaira–Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes" by Bershadsky, Cecotti, Ooguri, and Vafa (arxiv) on pg. 96 appear the two numbers $5760$ and $1451520$ related to integrals over moduli spaces of Riemann surfaces of genus $g=2$ and genus $3$ computed from certain quantities related to Chow rings. The associated numbers $2880$ and $90720$ in Vafa et al. are in Table 10, pg. 418, of "Chow rings of moduli spaces of curves I: The Chow ring of $\overline{\mathcal{M}}_3$" by C. Faber (JSTOR) and give $2 \cdot 2880 = 5760$ and $2^4 \cdot 90720 = 1451520.$

The numbers appear in OEIS A013524 as the denominators of the expansion

$$\tanh(\tan(x/2)) = \frac{1}{2}x - \frac{1}{480} x^5 - \frac{1}{5760} x^7 - \frac{1}{1451520} x^9 + \frac{13}{9676800} x^{11} + \cdots.$$

Not being familiar with the concepts, I was not able to come up with any references that presented results for any other genera.

Is this mere coincidence; that is, have computations for higher order genera been done, and, if so, are they included in this expansion?