Triangle Larch

triangle Larch    row sums [[|ShortAster]]
k n	0	1	2	3	4	5	6	7	8	9	sums
0	1										1
1	1	1									2
2	2	3	1								6
3	6	12	7	1							26
4	26	64	52	15	1						158
5	158	460	476	204	31	1					1330
6	1330	4464	5596	3180	780	63	1				15414
7	15414	58604	86308	61196	20940	2988	127	1			245578
8	245578	1043968	1767972	1505596	666316	141612	11564	255	1		5382862
9	5382862	25327980	48554444	48385900	26414892	7591340	997740	45228	511	1	162700898

Larch = Birch ∘ Pascal            compare Oak = Pascal ∘ Birch

This triangle may not be important. But it seems interesting, because Aster appears both as its left column and (shortened) as its row sums.

This is the inverse of Larch:   Larch⁻¹ = Pascal⁻¹ ∘ Birch⁻¹
The inverse of Birch is SignedEukalyptus.