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

%I A247358 #15 Jan 24 2022 04:35:06
%S A247358 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 A247358 256,1,8,49,128,216,625,729,1024,1,9,64,256,343,1296,2187,3125,4096,1,
%U A247358 10,81,512,512,2401,6561,7776,15625,16384,1,11,100,729,1024,4096,16807,19683,46656,65536,78125
%N A247358 Triangle read by rows: n-th row contains powers b^e with b + e = n + 1 in natural order.
%C A247358 Sorted rows of triangle A051129.
%H A247358 Reinhard Zumkeller, <a href="/A247358/b247358.txt">Rows n = 1..125 of triangle, flattened</a>
%e A247358 .  1  |  1                            |  1^1
%e A247358 .  2  |  1 2                          |  1^2 2^1
%e A247358 .  3  |  1 3  4                       |  1^3 3^1 2^2
%e A247358 .  4  |  1 4  8   9                   |  1^4 4^1 2^3 3^2
%e A247358 .  5  |  1 5 16  16  27               |  1^5 5^1 2^4 4^2 3^3
%e A247358 .  6  |  1 6 25  32  64  81           |  1^6 6^1 5^2 2^5 4^3 3^4
%e A247358 .  7  |  1 7 36  64 125 243 256       |  1^7 7^1 6^2 2^6 5^3 3^5 4^4
%e A247358 .  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 A247358 Table[Table[k^(n-k+1), {k, 1, n}] // Sort, {n, 1, 11}] // Flatten (* _Jean-François Alcover_, Nov 18 2019 *)
%o A247358 (Haskell)
%o A247358 import Data.List (sort)
%o A247358 a247358 n k = a247358_tabl !! (n-1) !! (k-1)
%o A247358 a247358_row n = a247358_tabl !! (n-1)
%o A247358 a247358_tabl = map sort a051129_tabl
%o A247358 (Python)
%o A247358 from itertools import chain
%o A247358 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 A247358 (PARI) row(n) = vecsort(vector(n, k, k^(n-k+1))); \\ _Michel Marcus_, Jan 24 2022
%Y A247358 Cf. A051129, A003101 (row sums), A247363 (central terms), A003320 (row maxima).
%K A247358 nonn,tabl
%O A247358 1,3
%A A247358 _Reinhard Zumkeller_, Sep 14 2014