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We solve the problem of the computation of the orbifold Euler characteristics of _g,n. We take the works of Harer-Zagier and Bini-Harer as our starting point, and apply the formalisms developed in and to this problem. These formalisms are typical examples of mathematical methods inspired by quantum field theories. We also present many closed formulas and some numerical data. In genus zero the results are related to Ramanujan polynomials, and in higher genera we get recursion relations almostarXiv:1812.10638v2 fatcat:zk77f7bcovhkpd6xb4dgeicosq