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A321707 Number of genus 7 rooted hypermaps with n darts. 2
10897286400, 1560315052800, 117805728533760, 6234567636407040, 259518044572234560, 9042873557130178560, 274213957041780607040, 7429773263737371426000, 183321599847270732775284, 4178263675886440605897708, 88944569813776527012125700, 1783998282211666387087167804 (list; graph; refs; listen; history; text; internal format)
OFFSET

15,1

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 15..115

Peter Zograf, Enumeration of Grothendieck's Dessins and KP Hierarchy, arXiv:1312.2538 [math.CO], 2014.

FORMULA

G.f.: y*(y - 1)^15*(65934428*y^29 - 2373639408*y^28 + 78065287272*y^27 - 1239982167455*y^26 + 15824435903631*y^25 - 147973440711114*y^24 + 1121119206347992*y^23 - 6897821674771866*y^22 + 35411504747483046*y^21 - 153195355715747532*y^20 + 564430051160248776*y^19 - 1782487694948370405*y^18 + 4847762532445875077*y^17 - 11385796789588847190*y^16 + 23121306258262005552*y^15 - 40583304876425900476*y^14 + 61456131914028384816*y^13 - 80013191284851054552*y^12 + 89093563965211655640*y^11 - 84217909084706439705*y^10 + 66908561791095714729*y^9 - 44081770356535124534*y^8 + 23656775380308201720*y^7 - 10093706157332984394*y^6 + 3311499493215102574*y^5 - 796565568171137388*y^4 + 130914104820311544*y^3 - 13151257876934851*y^2 + 664822027105443*y - 11057829184170)/(2*(y - 2)^32*(y + 1)^25), where y=A000108(2*x).

PROG

(PARI)

seq(N) = {

  my(x='x+O('x^(N+2)), y=(1-sqrt(1-8*x))/(4*x));

  Vec(y*(y - 1)^15*(65934428*y^29 - 2373639408*y^28 + 78065287272*y^27 - 1239982167455*y^26 + 15824435903631*y^25 - 147973440711114*y^24 + 1121119206347992*y^23 - 6897821674771866*y^22 + 35411504747483046*y^21 - 153195355715747532*y^20 + 564430051160248776*y^19 - 1782487694948370405*y^18 + 4847762532445875077*y^17 - 11385796789588847190*y^16 + 23121306258262005552*y^15 - 40583304876425900476*y^14 + 61456131914028384816*y^13 - 80013191284851054552*y^12 + 89093563965211655640*y^11 - 84217909084706439705*y^10 + 66908561791095714729*y^9 - 44081770356535124534*y^8 + 23656775380308201720*y^7 - 10093706157332984394*y^6 + 3311499493215102574*y^5 - 796565568171137388*y^4 + 130914104820311544*y^3 - 13151257876934851*y^2 + 664822027105443*y - 11057829184170)/(2*(y - 2)^32*(y + 1)^25));

};

seq(12)

CROSSREFS

Column 7 of A321710.

Sequence in context: A135047 A017541 A112453 * A246286 A295464 A095426

Adjacent sequences:  A321704 A321705 A321706 * A321708 A321709 A321710

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Nov 17 2018

STATUS

approved

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Last modified October 6 03:14 EDT 2022. Contains 357261 sequences. (Running on oeis4.)