A110138 a(n) = ceiling(n/2)^floor(n/2).

1, 1, 1, 2, 4, 9, 27, 64, 256, 625, 3125, 7776, 46656, 117649, 823543, 2097152, 16777216, 43046721, 387420489, 1000000000, 10000000000, 25937424601, 285311670611, 743008370688, 8916100448256, 23298085122481, 302875106592253, 793714773254144, 11112006825558016

Offset: 0

Author

Paul Barry, Jul 13 2005

Keywords

• easy
• nonn

Comments

a(n) is the number of partitions of [n] such that each block has exactly one odd element: a(5) = 9: 124|3|5, 12|34|5, 12|3|45, 14|23|5, 1|234|5, 1|23|45, 14|25|3, 1|245|3, 1|25|34. - Alois P. Heinz, Jun 01 2023

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..773

Crossrefs

Cf. A000312, A110132.

Programs

Python

def A110138(n): return ((m:=n>>1)+(n&1))**m # Chai Wah Wu, Jan 18 2023

Formula

a(2n) = A110132(2n) = A000312(n).