A247358 Triangle read by rows: n-th row contains powers b^e with b + e = n + 1 in natural order.

1, 1, 2, 1, 3, 4, 1, 4, 8, 9, 1, 5, 16, 16, 27, 1, 6, 25, 32, 64, 81, 1, 7, 36, 64, 125, 243, 256, 1, 8, 49, 128, 216, 625, 729, 1024, 1, 9, 64, 256, 343, 1296, 2187, 3125, 4096, 1, 10, 81, 512, 512, 2401, 6561, 7776, 15625, 16384, 1, 11, 100, 729, 1024, 4096, 16807, 19683, 46656, 65536, 78125

Offset: 1

Author

Reinhard Zumkeller, Sep 14 2014

Keywords

• nonn
• tabl

Comments

Sorted rows of triangle A051129.

Examples

			.  1  |  1                            |  1^1
.  2  |  1 2                          |  1^2 2^1
.  3  |  1 3  4                       |  1^3 3^1 2^2
.  4  |  1 4  8   9                   |  1^4 4^1 2^3 3^2
.  5  |  1 5 16  16  27               |  1^5 5^1 2^4 4^2 3^3
.  6  |  1 6 25  32  64  81           |  1^6 6^1 5^2 2^5 4^3 3^4
.  7  |  1 7 36  64 125 243 256       |  1^7 7^1 6^2 2^6 5^3 3^5 4^4
.  8  |  1 8 49 128 216 625 729 1024  |  1^8 8^1 7^2 2^7 6^3 5^4 3^6 4^5 .
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A051129, A003101 (row sums), A247363 (central terms), A003320 (row maxima).

Programs

Haskell

import Data.List (sort)
a247358 n k = a247358_tabl !! (n-1) !! (k-1)
a247358_row n = a247358_tabl !! (n-1)
a247358_tabl = map sort a051129_tabl

Mathematica

Table[Table[k^(n-k+1), {k, 1, n}] // Sort, {n, 1, 11}] // Flatten (* Jean-François Alcover, Nov 18 2019 *)

PARI

row(n) = vecsort(vector(n, k, k^(n-k+1))); \\ Michel Marcus, Jan 24 2022

Python

from itertools import chain
A247358_list = list(chain.from_iterable(sorted((b+1)**(n-b) for b in range(n)) for n in range(1,8))) # Chai Wah Wu, Sep 14 2014