|
|
|
|
1, 1, 3, 15, 176, 6842, 1505499, 3913864295, 338854264248680, 4216199393504640098482, 59475094770587936660132803278445, 17618334934720173062514849536736413843694654543
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
The partition numbers have an apparent fractal-like structure starting with every term in A173301.
Let A000041 = row 0, then under every (2^n - 1)-th term, begin a new row with the partition numbers; then take finite differences of each column from below.
The sum of finite difference terms will reproduce the partition numbers, with finite difference rows (starting from the top going down) = number of partitions of n that do not contain (1, 2, 3,...). (Cf. the array shown in A173302).
|
|
REFERENCES
|
Refer to tables of the partition numbers.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = A000041(2^n - 1), n = (0, 1, 2,...).
|
|
MATHEMATICA
|
Table[PartitionsP[2^n - 1], {n, 0 , 10}] (* Amiram Eldar, Feb 26 2020 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|