Dear all,

The problem is solved by using the namespace of lua as below:

I am not sure what I did is the right way.

If it is not the right way, please let me know.

Thanks for reading.

Best regards,

Dalyoung

\startluacode
P={}
combi = P

function P.fact (n)
  if n <= 0 then
    return 1
  else
    return n * P.fact(n-1)
  end
end

function P.ncr(n,r)
   return P.fact(n)/(P.fact(r)*P.fact(n-r))
end
combi = {
   fact = fact,
   ncr = ncr,
}
\stopluacode

\startbuffer[fig121]
numeric n,r,s,u,dx,dy,tt; u := 1.8cm;
path p, q;
pair A,B,start,now;
A := dir(210)*u;
B := dir(-30)*u;
dy := sind(30)*u;
dx := 2*cosd(30)*u;
for n=0 upto 4:
   start := n*dir(210)*u;
   for r=0 upto n:
      s := n-r;
%     tt := lua("mp.print(P.fact(" & decimal n & ")/(P.fact(" & decimal r & ")*P.fact(" & decimal s &" )))");
      tt := lua("mp.print(P.ncr(" & decimal n & "," &  decimal r & " ))");
      now := start+r*right*dx;
      dotlabel.top(textext("$\displaystyle {" & decimal n & "\choose" & decimal r & "} = "& decimal tt & "$"),now);
      draw now -- (now+A);
      draw now -- (now+B);
   endfor;
endfor;
\stopbuffer