Question 9
For every pair of positive integers \((x,y)\), define \(f(x,y)\) by
\[f(x,1)=x,\qquad f(x,y)=0\quad\text{if }y\gt x,\]
\[f(x+1,y)=y[f(x,y)+f(x,y-1)].\]
Evaluate \(f(5,5)\).
Editorial boundary convention: use the recurrence for \(y\ge2\); the first formula gives the \(y=1\) boundary values. The source does not state that recurrence restriction explicitly.
\[f(x,1)=x,\qquad f(x,y)=0\quad\text{if }y\gt x,\]
\[f(x+1,y)=y[f(x,y)+f(x,y-1)].\]
Evaluate \(f(5,5)\).
Editorial boundary convention: use the recurrence for \(y\ge2\); the first formula gives the \(y=1\) boundary values. The source does not state that recurrence restriction explicitly.