References : 
http://myweb.facstaff.wwu.edu/trenees/Math_566/stirling.pdf
http://mathworld.wolfram.com/Partition.html
 http://planetmath.org/sites/default/files/texpdf/32805.pdf
https://www.google.com/searchq=stirling+numbers+of+a+second+kind+images&biw=1366&bih=667&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiaotS3kcnKAhUW4WMKHUuiBXgQ_AUIBigB#tbm=isch&q=stirling+numbers+of+first+kind&imgrc=6vfPkyD0D3AL4M%3A  
https://www.google.com/searchq=stirling+numbers+of+a+second+kind+images&biw=1366&bih=667&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiaotS3kcnKAhUW4WMKHUuiBXgQ_AUIBigB#imgrc=KPxTbUiREv8g_M%3A