A122391 - cp's OEIS frontend

A122391 Dimension of 2-variable non-commutative harmonics (Hausdorff derivative). The dimension of the space of non-commutative polynomials in 2 variables which are killed by all symmetric differential operators (where for a monomial w, d_{xi} ( w ) = sum over all subwords of w deleting xi once).

n	a(n)
0	1
1	1
2	1
3	3
4	6
5	12
6	24
7	48
8	96
9	192
10	384
11	768
12	1536
13	3072
14	6144
15	12288
16	24576
17	49152
18	98304
19	196608
20	393216
21	786432
22	1572864
23	3145728
24	6291456
25	12582912
26	25165824
27	50331648
28	100663296
29	201326592
30	402653184
31	805306368
32	1610612736
33	3221225472
34	6442450944
35	12884901888
36	25769803776

[1, 1, 1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472, 6442450944, 12884901888, 25769803776]

cp's OEIS Frontend

A122391 Dimension of 2-variable non-commutative harmonics (Hausdorff derivative). The dimension of the space of non-commutative polynomials in 2 variables which are killed by all symmetric differential operators (where for a monomial w, d_{xi} ( w ) = sum over all subwords of w deleting xi once).

Table of values

List of values