A365881 Number of partitions of 2^(2n) into 2^n parts.

1, 2, 34, 55974, 676491536028, 406965070979714742549848209, 597255854605931071381819520057048465533319700618519238060

Offset: 0

Author

Alois P. Heinz, Sep 21 2023

Keywords

• nonn

Comments

Also number of partitions of 2^(2n) where the largest part is 2^n. a(2) = 34: 4111111111111, 421111111111, 42211111111, 4222111111, 422221111, 42222211, 4222222, 43111111111, 4321111111, 432211111, 43222111, 4322221, 433111111, 43321111, 4332211, 433222, 4333111, 433321, 43333, 4411111111, 442111111, 44221111, 4422211, 442222, 44311111, 4432111, 443221, 443311, 44332, 4441111, 444211, 44422, 44431, 4444.

Examples

			a(0) = 1: 1.
a(1) = 2: 22, 31.
a(2) = 34: 4444, 5443, 5533, 5542, 5551, 6433, 6442, 6532, 6541, 6622, 6631, 7333, 7432, 7441, 7522, 7531, 7621, 7711, 8332, 8422, 8431, 8521, 8611, 9322, 9331, 9421, 9511, (10)222, (10)321, (10)411, (11)221, (11)311, (12)211, (13)111.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..9 (n = 0..8 from Alois P. Heinz)

Crossrefs

Cf. A000079, A000302, A008284, A327483.

Programs

Python

# uses A008284_T
def A365881(n): return A008284_T((m:=1<Chai Wah Wu, Sep 22 2023

Formula

a(n) = A327483(2n,n).

a(n) = A008284(4^n,2^n).