A173301 a(n) = A000041(2^n - 1).

1, 1, 3, 15, 176, 6842, 1505499, 3913864295, 338854264248680, 4216199393504640098482, 59475094770587936660132803278445, 17618334934720173062514849536736413843694654543

Offset: 0

Author

Gary W. Adamson, Feb 15 2010

Keywords

• nonn

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

• Amiram Eldar, Table of n, a(n) for n = 0..19

Crossrefs

Cf. A000041, A000225, A002865, A027336, A173302.

Programs

Mathematica

Table[PartitionsP[2^n - 1], {n, 0 ,10}] (* Amiram Eldar, Feb 26 2020 *)

Formula

a(n) = A000041(2^n - 1), n = (0, 1, 2,...).

a(n) = A000041(A000225(n)). - Omar E. Pol, Oct 29 2013