Poisson race distribution/CalcTable1

[ilmath]k[/ilmath]	[ilmath]X[/ilmath]	[ilmath]Y[/ilmath]
[ilmath]0[/ilmath]	[ilmath]X\eq 0[/ilmath]	[ilmath]Y\eq 0[/ilmath]
	[ilmath]X\eq 1[/ilmath]	[ilmath]Y\eq 1[/ilmath]
	[ilmath]X\eq 2[/ilmath]	[ilmath]Y\eq 2[/ilmath]
	[ilmath]\vdots[/ilmath]	[ilmath]\vdots[/ilmath]
	[ilmath]X\eq i[/ilmath]	[ilmath]Y\eq i[/ilmath]
[ilmath]1[/ilmath]	[ilmath]X\eq 1[/ilmath]	[ilmath]Y\eq 0[/ilmath]
	[ilmath]X\eq 2[/ilmath]	[ilmath]Y\eq 1[/ilmath]
	[ilmath]X\eq 3[/ilmath]	[ilmath]Y\eq 2[/ilmath]
	[ilmath]\vdots[/ilmath]	[ilmath]\vdots[/ilmath]
	[ilmath]X\eq i+1[/ilmath]	[ilmath]Y\eq i[/ilmath]
[ilmath]2[/ilmath]	[ilmath]X\eq 2[/ilmath]	[ilmath]Y\eq 0[/ilmath]
	[ilmath]X\eq 3[/ilmath]	[ilmath]Y\eq 1[/ilmath]
	[ilmath]X\eq 4[/ilmath]	[ilmath]Y\eq 2[/ilmath]
	[ilmath]\vdots[/ilmath]	[ilmath]\vdots[/ilmath]
	[ilmath]X\eq i+2[/ilmath]	[ilmath]Y\eq i[/ilmath]
[ilmath]\cdots[/ilmath]
[ilmath]j[/ilmath]	[ilmath]X\eq j[/ilmath]	[ilmath]Y\eq 0[/ilmath]
	[ilmath]X\eq j+1[/ilmath]	[ilmath]Y\eq 1[/ilmath]
	[ilmath]X\eq j+2[/ilmath]	[ilmath]Y\eq 2[/ilmath]
	[ilmath]\vdots[/ilmath]	[ilmath]\vdots[/ilmath]
	[ilmath]X\eq i+j[/ilmath]	[ilmath]Y\eq i[/ilmath]

This shows why we sum over what we sum over!