The coefficient of xr in the expansion of (1+3x+6x2+10x3+......) is :
(r+1)
(r+1)/2
(r+1)(r+2)/2
(r+2)/2
(1+3x+6x2+10x3+...)=(1−x)−3
∴ Coefficient of xr=3+r−1Cr=r+2C2
= 12(r+2)(r+1)