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.: arctan(x*(1 - y)/sqrt((1 - 2*x)*(1 - 2*x*y)))/(1 - y)/sqrt(1 - 2*x).
EXAMPLE
Triangle begins:
1;
4, 2;
22, 16, 7;
160, 136, 88, 36;
1464, 1344, 1044, 624, 249;
...
For n = 2 and k = 1, let the four vertices be {1,2,3,4}. The marked chord can either be (1,2) and it excludes one other chord, namely (3,4), or vice-versa, hence T(2,1) = 2.
MATHEMATICA
CoefficientList[Normal[Series[1/(1-y)/Sqrt[1-2*x]*ArcTan[(x*(1-y))/Sqrt[(1-2*x)]/Sqrt[1-2*y*x]], {x, 0, 10}]]/.{x^n_.->x^n*n!}, {x, y}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Donovan Young, Jul 31 2020
STATUS
approved