A110132 a(n) = floor(n/2)^ceiling(n/2).

1, 0, 1, 1, 4, 8, 27, 81, 256, 1024, 3125, 15625, 46656, 279936, 823543, 5764801, 16777216, 134217728, 387420489, 3486784401, 10000000000, 100000000000, 285311670611, 3138428376721, 8916100448256, 106993205379072, 302875106592253, 3937376385699289

Offset

0,5

Comments

Central coefficients T(n,floor(n/2)) of number triangle A004248. The central coefficients T(2n,n) of this triangle are n^n or A000312.

a(n) is the number of partitions of [n] such that each block has exactly one even element: a(5) = 8: 1235|4, 123|45, 125|34, 12|345, 1345|2, 134|25, 145|23, 14|235. - Alois P. Heinz, Jun 01 2023

Links

Alois P. Heinz, Table of n, a(n) for n = 0..772

Formula

Sum_{n>=2} 1/a(n) = A073009 + A135608 + 1. - Amiram Eldar, Jan 22 2026

Mathematica

Join[{1}, Table[Floor[n/2]^Ceiling[n/2], {n, 30}]] (* Harvey P. Dale, Feb 16 2025 *)

Crossrefs

Cf. A000312, A004248, A110138.

Cf. A073009, A135608.

Sequence in context: A279627 A026085 A036720 * A099513 A104042 A338429

Adjacent sequences: A110129 A110130 A110131 * A110133 A110134 A110135

Keyword

easy,nonn

Author

Paul Barry, Jul 13 2005

Status

approved