| triangle Birch (~A139382) row sums Aster (A135922)
|
k n |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
sums
|
| 0
|
1
|
|
|
|
|
|
|
|
1
|
| 1
|
0
|
1
|
|
|
|
|
|
|
1
|
| 2
|
0
|
1
|
1
|
|
|
|
|
|
2
|
| 3
|
0
|
1
|
4
|
1
|
|
|
|
|
6
|
| 4
|
0
|
1
|
13
|
11
|
1
|
|
|
|
26
|
| 5
|
0
|
1
|
40
|
90
|
26
|
1
|
|
|
158
|
| 6
|
0
|
1
|
121
|
670
|
480
|
57
|
1
|
|
1330
|
| 7
|
0
|
1
|
364
|
4811
|
7870
|
2247
|
120
|
1
|
15414
|
as side of pyramid Ivy
n: adicity = valency
k: depth
- T(n,k) = (2^k-1) * T(n-1,k) + T(n-1,k-1)
- second diagonal: Eulerian numbers A000295 a(n) = 2^n - n - 1 (see also A125128, A130103)
- column 2: A003462 a(n) = (3^n - 1)/2
- column 3: A016212 a(n) = (7^(n+2) - 3^(n+3) + 2)/24
