A067735 - OEIS

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A067735

Number of partitions of 2^n into distinct parts.

1, 1, 2, 6, 32, 390, 16444, 4013544, 11784471548, 1168225267521350, 16816734263788624008200, 276565526698898057002583240473088, 96052644365764024805972019009272150642974291708, 43586702014259316987395017345466711329303914541873541942193666197800

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OFFSET

0,3

COMMENTS

Always even for n>1 since the only powers of two which are generalized pentagonal numbers (A001318 - needed to produce odd numbers of partitions into distinct terms) are 2^0 and 2^1. Number of digits of A068413 divided by number of digits of a(n) approaches sqrt(2).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..14

Henry Bottomley, Partition calculators using java applets

Index entries for sequences related to partitions

FORMULA

a(n) = A000009(A000079(n)).

a(n) ~ exp(Pi*sqrt(2^n/3))/(3^(1/4)*2^(3*n/4+2)). - Ilya Gutkovskiy, Jan 13 2017

EXAMPLE

a(3)=6 since 2^3=8 can be partitioned into 8, 7+1, 6+2, 5+3, 5+2+1, or 4+3+1.

MATHEMATICA

Table[ PartitionsQ[2^n], {n, 0, 13}]

CROSSREFS