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

1, 1, 3, 15, 105, 945, 3465, 14857, 72905, 393565, 2152693, 10317169, 49808117, 247455873, 1256019673, 6371895677, 31696702545, 157383838325, 785587613797, 3938599251649, 19742522444733, 98655068282297, 492637126850897, 2462204077446773, 12316715419452585

Offset: 0

Author

Alois P. Heinz, Oct 21 2017

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3, 4, 2, 81, 495, -648, -1590, 208, -5670, -924, 14576, -1536, -2136, -9936, 10656, -2880)

Crossrefs

Column k=5 of A293960.

Programs

Mathematica

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 *)

Formula

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)).