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A173301 a(n) = A000041(2^n - 1), n = (0, 1, 2,...) 3
1, 1, 3, 15, 176, 6842, 1505499, 3913864295, 338854264248680, 4216199393504640098482 (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

Table of n, a(n) for n=0..9.

FORMULA

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

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

CROSSREFS

Cf. A000041, A173302, A002865, A027336.

Sequence in context: A059386 A077792 A153079 * A260079 A087614 A063739

Adjacent sequences:  A173298 A173299 A173300 * A173302 A173303 A173304

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Feb 15 2010

STATUS

approved

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Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)