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A078707 Number of vectors of length n that are symmetric about the middle, where each element is drawn from a set of n distinct elements. 4
1, 1, 2, 9, 16, 125, 216, 2401, 4096, 59049, 100000, 1771561, 2985984, 62748517, 105413504, 2562890625, 4294967296, 118587876497, 198359290368, 6131066257801, 10240000000000, 350277500542221, 584318301411328, 21914624432020321, 36520347436056576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This might be called the "ceiling factorial of n" (see the "additional information" link). - R. J. Cano, Jun 17 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

R. J. Cano, Additional information

FORMULA

a(n) = n^(floor((n+1)/2)) = n^ceiling(n/2).

EXAMPLE

Examples added by N. J. A. Sloane, Jun 17 2014:

n=1: 1 (1).

n=2: 11, 22 (2).

n=3: 111X3, 121X6 (9).

n=4: 1111X4, 1221X12 (16).

n=5: 11111X5, 11211X20, 12221X20, 12121X20, 12321X60 (125).

MAPLE

a:= n-> n^ceil(n/2): seq(a(n), n=0..30);  # Alois P. Heinz, Jul 23 2014

MATHEMATICA

Join[{1}, Table[n^Ceiling[n/2], {n, 30}]] (* Wesley Ivan Hurt, Jan 15 2017 *)

PROG

(PARI) for(n=1, 22, print1(n^((n+n%2)/2), ", "))

CROSSREFS

Cf. A004526, A243520.

Cf. A168658, A275549.

Sequence in context: A032136 A032040 A045661 * A085332 A204424 A062981

Adjacent sequences:  A078704 A078705 A078706 * A078708 A078709 A078710

KEYWORD

nonn,easy

AUTHOR

Mark Sterling, Dec 18 2002

EXTENSIONS

Extended by Klaus Brockhaus, Dec 19 2002

a(0)=1 inserted by Alois P. Heinz, Jul 23 2014

STATUS

approved

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Last modified February 28 09:52 EST 2020. Contains 332323 sequences. (Running on oeis4.)