cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A321707 Number of genus 7 rooted hypermaps with n darts.

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%I A321707 #11 Dec 17 2018 19:13:04
%S A321707 10897286400,1560315052800,117805728533760,6234567636407040,
%T A321707 259518044572234560,9042873557130178560,274213957041780607040,
%U A321707 7429773263737371426000,183321599847270732775284,4178263675886440605897708,88944569813776527012125700,1783998282211666387087167804
%N A321707 Number of genus 7 rooted hypermaps with n darts.
%H A321707 Gheorghe Coserea, <a href="/A321707/b321707.txt">Table of n, a(n) for n = 15..115</a>
%H A321707 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 A321707 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).
%o A321707 (PARI)
%o A321707 seq(N) = {
%o A321707   my(x='x+O('x^(N+2)), y=(1-sqrt(1-8*x))/(4*x));
%o A321707   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));
%o A321707 };
%o A321707 seq(12)
%Y A321707 Column 7 of A321710.
%K A321707 nonn
%O A321707 15,1
%A A321707 _Gheorghe Coserea_, Nov 17 2018