A365881 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A365881

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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.

LINKS

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

FORMULA

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

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

EXAMPLE

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.

PROG

(Python)

# uses A008284_T

def A365881(n): return A008284_T((m:=1<<n)**2, m) # Chai Wah Wu, Sep 22 2023

CROSSREFS

Cf. A000079, A000302, A008284, A327483.

Sequence in context: A155205 A303444 A230244 * A045529 A293245 A077747

Adjacent sequences: A365878 A365879 A365880 * A365882 A365883 A365884

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 21 2023

STATUS

approved