A068413 a(n) = number of partitions of 2^n.

1, 2, 5, 22, 231, 8349, 1741630, 4351078600, 365749566870782, 4453575699570940947378, 61847822068260244309086870983975, 18116048323611252751541173214616030020513022685, 6927233917602120527467409170319882882996950147283323368445315320451

Offset: 0

Author

Henry Bottomley, Mar 03 2002

Keywords

• nonn

Examples

			a(2)=5 since there are 5 partitions of 2^2=4: 4, 3+1, 2+2, 2+1+1, 1+1+1+1+1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..19
• Henry Bottomley, Partition calculators using java applets
• Index entries for sequences related to partitions

Crossrefs

Cf. A000041, A000079, A018819, A067735.

Programs

Mathematica

Table[ PartitionsP[2^n], {n, 0, 12}]

Formula

a(n) = A000041(A000079(n)).

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