A321705 Number of genus 5 rooted hypermaps with n darts.

604800, 57170880, 2936606400, 108502598960, 3225186125460, 81861294718764, 1840409325096500, 37558997857897164, 708015469597497732, 12488421105878928700, 208161512148250424484, 3304395638081490531324, 50267199680265668419244, 736516493829967530909204, 10437808798822929984593100

Offset: 11

Author

Gheorghe Coserea, Nov 17 2018

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 11..111
• 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 7
• Peter Zograf, Enumeration of Grothendieck's Dessins and KP Hierarchy, arXiv:1312.2538 [math.CO], 2014.

Crossrefs

Column 5 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)^11*(13150*y^19 - 315600*y^18 + 6947865*y^17 - 70489470*y^16 + 569637816*y^15 - 3253135788*y^14 + 14658702716*y^13 - 51696766668*y^12 + 146255446788*y^11 - 332779761068*y^10 + 610739916966*y^9 - 900544355928*y^8 + 1057440629016*y^7 - 973453624356*y^6 + 685359139356*y^5 - 355019010868*y^4 + 127180243662*y^3 - 28342783668*y^2 + 3224985513*y - 120590634)/(4*(y - 2)^22*(y + 1)^17));
};
seq(15)

Formula

G.f.: y*(y - 1)^11*(13150*y^19 - 315600*y^18 + 6947865*y^17 - 70489470*y^16 + 569637816*y^15 - 3253135788*y^14 + 14658702716*y^13 - 51696766668*y^12 + 146255446788*y^11 - 332779761068*y^10 + 610739916966*y^9 - 900544355928*y^8 + 1057440629016*y^7 - 973453624356*y^6 + 685359139356*y^5 - 355019010868*y^4 + 127180243662*y^3 - 28342783668*y^2 + 3224985513*y - 120590634)/(4*(y - 2)^22*(y + 1)^17), where y=A000108(2*x).