4,1

Tree-rooted planar maps are counted by A005568, and tree-rooted maps on the torus by A118445.

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.

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.

Sequence in context: A012211 A036059 A036519 this_sequence A130332 A035319 A081786

Adjacent sequences: A118443 A118444 A118445 this_sequence A118447 A118448 A118449

nonn

Valery A. Liskovets (liskov(AT)im.bas-net.by), May 04 2006