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REFERENCES
| T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. II, J. Comb. Theory, Ser. B, 13, No. 2 (1972), 122-141 (pp. 137, 140).
E. A. Bender, E. R. Canfield and R. W. Robinson, The asymptotic number of tree-rooted maps on a surface, J. Comb. Theory, Ser. A, 48, No. 2 (1988), 156-164.
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FORMULA
| a(n)=binomial(2n,0)C(0)b(n)+binomial(2n,2)C(1)b(n-1) +binomial(2n,4)C(2)b(n-2)+...+binomial(2n,2n)C(n)b(0), where C(n)=A000108(n) - n-th Catalan number and b(n)=A006298(n) - the number of one-vertex maps of genus 2 for n>=4 and b(n)=0 for n<4.
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