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A118445 Number of tree-rooted maps of genus 1 with n edges: rooted maps on the torus with a distinguished spanning tree. 1
1, 25, 490, 8820, 152460, 2576574, 42942900, 709171320, 11636856660, 190068658780, 3093732938296, 50222937310000, 813611584422000, 13158602740363500, 212528020730913000, 3428785401125396400, 55266606794455402500, 890117467077758188500 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=2..19.

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.

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).

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) = (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.

O.g.f.: x^2 * hypergeom([5/2, 5/2], [4], 16*x).  - Mark van Hoeij, Apr 06 2013

MATHEMATICA

HypergeometricPFQ[{5/2, 5/2}, {4}, 16x] + O[x]^18 // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Aug 28 2019 *)

CROSSREFS

Sequence in context: A089386 A014927 A059946 * A000497 A028341 A282689

Adjacent sequences:  A118442 A118443 A118444 * A118446 A118447 A118448

KEYWORD

nonn

AUTHOR

Valery A. Liskovets, May 04 2006

EXTENSIONS

Added more terms, Joerg Arndt, Apr 07 2013

STATUS

approved

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Last modified August 12 05:33 EDT 2020. Contains 336438 sequences. (Running on oeis4.)