Problem 43754. Lah Numbers

Create a square lower diagonal matrix containing the first n Lah number coefficients. In mathematics, the Lah numbers are coefficients expressing rising factorials in terms of falling factorials. For example, for n=8, the matrix of Lah numbers would be:

1	0	0	0	0	0	0	0	0	0	0
2	1	0	0	0	0	0	0	0	0	0
6	6	1	0	0	0	0	0	0	0	0
24	36	12	1	0	0	0	0	0	0	0
120	240	120	20	1	0	0	0	0	0	0
720	1800	1200	300	30	1	0	0	0	0	0
5040	15120	12600	4200	630	42	1	0	0	0	0
40320	141120	141120	58800	11760	1176	56	1	0	0	0
362880	1451520	1693440	846720	211680	28224	2016	72	1	0	0

See Lah Number for more information.