OFFSET
1,2
LINKS
Donovan Young, Table of n, a(n) for n = 1..9870
Donovan Young, A critical quartet for queuing couples, arXiv:2007.13868 [math.CO], 2020.
FORMULA
E.g.f.: log((1 - x*(1 + y))/(1 - 2*x))/(1 - y)/sqrt(1 - 2*x).
EXAMPLE
Triangle begins:
1;
5, 1;
32, 11, 2;
260, 116, 38, 6;
2589, 1344, 594, 174, 24;
...
For n = 2 and k = 1, let the four vertices be {1,2,3,4}. The marked chord can only be (2,3) and it is contained by one other chord, namely (1,4), hence T(2,1) = 1.
MATHEMATICA
CoefficientList[Normal[Series[ CoefficientList[Normal[Series[Log[(1-x*(1+y))/(1-2*x)]/(1-y)/Sqrt[1-2*x], {x, 0, 10}]]/.{x^n_.->x^n*n!}, {x, y}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Donovan Young, Jul 30 2020
STATUS
approved