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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.

A293997 Number of linear chord diagrams having n chords and no chord length larger than five.

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%I A293997 #9 Jan 03 2024 09:12:13
%S A293997 1,1,3,15,105,945,3465,14857,72905,393565,2152693,10317169,49808117,
%T A293997 247455873,1256019673,6371895677,31696702545,157383838325,
%U A293997 785587613797,3938599251649,19742522444733,98655068282297,492637126850897,2462204077446773,12316715419452585
%N A293997 Number of linear chord diagrams having n chords and no chord length larger than five.
%H A293997 Alois P. Heinz, <a href="/A293997/b293997.txt">Table of n, a(n) for n = 0..1000</a>
%H A293997 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (3, 4, 2, 81, 495, -648, -1590, 208, -5670, -924, 14576, -1536, -2136, -9936, 10656, -2880)
%F A293997 G.f.: -(24*x^11-84*x^10+76*x^9+20*x^8-10*x^7-90*x^6+12*x^5+35*x^4+4*x^2+2*x-1) / ((5*x-1) *(576*x^15 -2016*x^14 +1584*x^13 +744*x^12 +456*x^11 -2824*x^10 -380*x^9 +1058*x^8 +170*x^7 +352*x^6 +200*x^5 -59*x^4 -28*x^3 -6*x^2 -2*x-1)).
%t A293997 CoefficientList[Series[-(24x^11-84x^10+76x^9+20x^8-10x^7-90x^6+12x^5+35x^4+4x^2+2x-1)/((5x-1)(576x^15-2016x^14+1584x^13+744x^12+ 456x^11- 2824x^10-380x^9+ 1058x^8+ 170x^7+352x^6+200x^5-59x^4-28x^3-6x^2-2x-1)),{x,0,30}],x] (* or *) LinearRecurrence[ {3,4,2,81,495,-648,-1590,208,-5670,-924,14576,-1536,-2136,-9936,10656,-2880},{1,1,3,15,105,945,3465,14857,72905,393565,2152693,10317169,49808117,247455873,1256019673,6371895677},30] (* _Harvey P. Dale_, Jan 03 2024 *)
%Y A293997 Column k=5 of A293960.
%K A293997 nonn,easy
%O A293997 0,3
%A A293997 _Alois P. Heinz_, Oct 21 2017