A321706 Number of genus 6 rooted hypermaps with n darts.

68428800, 8099018496, 511859777472, 22925949056640, 815521082030784, 24494440792190400, 645212095792089220, 15292175926873102956, 332150183310464271324, 6702637985834037183508, 126995200843857803023176, 2278149500006567629947864, 38954050134978747926573016

Offset: 13

Author

Gheorghe Coserea, Nov 17 2018

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 13..113
• Mednykh, A.; Nedela, R. Recent progress in enumeration of hypermaps, J. Math. Sci., New York 226, No. 5, 635-654 (2017) and Zap. Nauchn. Semin. POMI 446, 139-164 (2016), table 8
• Peter Zograf, Enumeration of Grothendieck's Dessins and KP Hierarchy, arXiv:1312.2538 [math.CO], 2014.

Crossrefs

Column 6 of A321710.

Programs

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)

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).