A067735 Number of partitions of 2^n into distinct parts.

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

Offset: 0

Author

Henry Bottomley, Mar 11 2002

Keywords

• nonn

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).

Examples

			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.
		

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

Crossrefs

Cf. A000009, A000079, A068413.

Programs

Mathematica

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

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