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Triangle read by rows: n-th row contains powers b^e with b + e = n + 1 in natural order.
5

%I #15 Jan 24 2022 04:35:06

%S 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,

%T 256,1,8,49,128,216,625,729,1024,1,9,64,256,343,1296,2187,3125,4096,1,

%U 10,81,512,512,2401,6561,7776,15625,16384,1,11,100,729,1024,4096,16807,19683,46656,65536,78125

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

%C Sorted rows of triangle A051129.

%H Reinhard Zumkeller, <a href="/A247358/b247358.txt">Rows n = 1..125 of triangle, flattened</a>

%e . 1 | 1 | 1^1

%e . 2 | 1 2 | 1^2 2^1

%e . 3 | 1 3 4 | 1^3 3^1 2^2

%e . 4 | 1 4 8 9 | 1^4 4^1 2^3 3^2

%e . 5 | 1 5 16 16 27 | 1^5 5^1 2^4 4^2 3^3

%e . 6 | 1 6 25 32 64 81 | 1^6 6^1 5^2 2^5 4^3 3^4

%e . 7 | 1 7 36 64 125 243 256 | 1^7 7^1 6^2 2^6 5^3 3^5 4^4

%e . 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 .

%t Table[Table[k^(n-k+1), {k, 1, n}] // Sort, {n, 1, 11}] // Flatten (* _Jean-François Alcover_, Nov 18 2019 *)

%o (Haskell)

%o import Data.List (sort)

%o a247358 n k = a247358_tabl !! (n-1) !! (k-1)

%o a247358_row n = a247358_tabl !! (n-1)

%o a247358_tabl = map sort a051129_tabl

%o (Python)

%o from itertools import chain

%o 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

%o (PARI) row(n) = vecsort(vector(n, k, k^(n-k+1))); \\ _Michel Marcus_, Jan 24 2022

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

%K nonn,tabl

%O 1,3

%A _Reinhard Zumkeller_, Sep 14 2014