|
%I #14 Aug 23 2022 14:11:54
%S 604800,57170880,2936606400,108502598960,3225186125460,81861294718764,
%T 1840409325096500,37558997857897164,708015469597497732,
%U 12488421105878928700,208161512148250424484,3304395638081490531324,50267199680265668419244,736516493829967530909204,10437808798822929984593100
%N Number of genus 5 rooted hypermaps with n darts.
%H Gheorghe Coserea, <a href="/A321705/b321705.txt">Table of n, a(n) for n = 11..111</a>
%H Mednykh, A.; Nedela, R. <a href="https://doi.org/10.1007/s10958-017-3555-5">Recent progress in enumeration of hypermaps</a>, J. Math. Sci., New York 226, No. 5, 635-654 (2017) and Zap. Nauchn. Semin. POMI 446, 139-164 (2016), table 7
%H Peter Zograf, <a href="https://arxiv.org/abs/1312.2538">Enumeration of Grothendieck's Dessins and KP Hierarchy</a>, arXiv:1312.2538 [math.CO], 2014.
%F 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).
%o (PARI)
%o seq(N) = {
%o my(x='x+O('x^(N+2)), y=(1-sqrt(1-8*x))/(4*x));
%o 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));
%o };
%o seq(15)
%Y Column 5 of A321710.
%K nonn
%O 11,1
%A _Gheorghe Coserea_, Nov 17 2018
| 