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Search: id:A118445
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| A118445 |
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Number of tree-rooted maps of genus 1 with n edges: rooted maps on the torus with a distinguished spanning tree. |
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+0
2
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| 1, 25, 490, 8820, 152460, 2576574, 42942900, 709171320, 11636856660, 190068658780
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Tree-rooted planar maps are counted by A005568, and tree-rooted maps of (orientable) genus 2 by A118446. Typically, a(11)=190068658780=2^2*5*7^2*11*13^2*17^2*19^2.
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REFERENCES
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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
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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)=(2n-1)!/(6(n-2)!(n-1)!)=A002802(n-2) - the number of toroidal one-vertex maps with n edges for n>=2 and b(0)=b(1)=0.
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CROSSREFS
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Adjacent sequences: A118442 A118443 A118444 this_sequence A118446 A118447 A118448
Sequence in context: A089386 A014927 A059946 this_sequence A000497 A028341 A122140
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KEYWORD
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nonn
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AUTHOR
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Valery A. Liskovets (liskov(AT)im.bas-net.by), May 04 2006
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