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A321706 Number of genus 6 rooted hypermaps with n darts. 2
68428800, 8099018496, 511859777472, 22925949056640, 815521082030784, 24494440792190400, 645212095792089220, 15292175926873102956, 332150183310464271324, 6702637985834037183508, 126995200843857803023176, 2278149500006567629947864, 38954050134978747926573016 (list; graph; refs; listen; history; text; internal format)
OFFSET

13,1

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 13..113

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

FORMULA

G.f.: -y*(y - 1)^13*(1080091*y^24 - 32402730*y^23 + 889296813*y^22 - 11575684382*y^21 + 120636055215*y^20 - 908735922846*y^19 + 5491340556019*y^18 - 26587756725282*y^17 + 105914199493428*y^16 - 349844034215428*y^15 + 966356094916770*y^14 - 2240740995310188*y^13 + 4368032453176430*y^12 - 7149882085566108*y^11 + 9789363335577126*y^10 - 11134972065337540*y^9 + 10413235525450707*y^8 - 7887398782084338*y^7 + 4736927774219617*y^6 - 2188131419800854*y^5 + 743586620967027*y^4 - 173682661266854*y^3 + 24974862235959*y^2 - 1816988020602*y + 43470403150)/(4*(y - 2)^27*(y + 1)^21), 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)^13*(1080091*y^24 - 32402730*y^23 + 889296813*y^22 - 11575684382*y^21 + 120636055215*y^20 - 908735922846*y^19 + 5491340556019*y^18 - 26587756725282*y^17 + 105914199493428*y^16 - 349844034215428*y^15 + 966356094916770*y^14 - 2240740995310188*y^13 + 4368032453176430*y^12 - 7149882085566108*y^11 + 9789363335577126*y^10 - 11134972065337540*y^9 + 10413235525450707*y^8 - 7887398782084338*y^7 + 4736927774219617*y^6 - 2188131419800854*y^5 + 743586620967027*y^4 - 173682661266854*y^3 + 24974862235959*y^2 - 1816988020602*y + 43470403150)/(4*(y - 2)^27*(y + 1)^21));

};

seq(13)

CROSSREFS

Column 6 of A321710.

Sequence in context: A230746 A084071 A251615 * A172608 A294989 A204405

Adjacent sequences:  A321703 A321704 A321705 * A321707 A321708 A321709

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Nov 17 2018

STATUS

approved

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Last modified May 20 02:46 EDT 2019. Contains 323412 sequences. (Running on oeis4.)