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A110138
a(n) = ceiling(n/2)^floor(n/2).
4
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
0,4
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
FORMULA
a(2n) = A110132(2n) = A000312(n).
PROG
(Python)
def A110138(n): return ((m:=n>>1)+(n&1))**m # Chai Wah Wu, Jan 18 2023
CROSSREFS
Sequence in context: A002773 A112706 A359502 * A148085 A003320 A007876
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 13 2005
STATUS
approved