%I #16 Jan 24 2022 04:35:19
%S 1,3,16,64,343,4096,59049,1000000,14348907,129140163,1475789056,
%T 38443359375,1099511627776,34271896307633,1156831381426176,
%U 42052983462257059,1152921504606846976,18446744073709551616,295147905179352825856,12116574790945106558976
%N Central terms of triangle A247358.
%C For all n there exist b(n) and e(n) such that: a(n)=b(n)^e(n) and b(n)+e(n)=2*n, see example.
%H Reinhard Zumkeller, <a href="/A247363/b247363.txt">Table of n, a(n) for n = 1..400</a>
%F a(n) = A247358(2*n-1,n).
%e . n | a(n) | b(n)^e(n) | b(n)+e(n)
%e . ----+-------------+-----------+----------
%e . 1 | 1 | 1^1 | 2
%e . 2 | 3 | 3^1 | 4
%e . 3 | 16 | 2^4 | 6
%e . 4 | 64 | 2^6 | 8
%e . 5 | 343 | 7^3 | 10
%e . 6 | 4096 | 8^4 | 12
%e . 7 | 59049 | 9^5 | 14
%e . 8 | 1000000 | 10^6 | 16
%e . 9 | 14348907 | 3^15 | 18
%e . 10 | 129140163 | 3^17 | 20
%e . 11 | 1475789056 | 14^8 | 22
%e . 12 | 38443359375 | 15^9 | 24
%o (Haskell)
%o a247363 n = a247358 (2 * n - 1) n
%o (Python)
%o def A247363(n):
%o ....return(sorted((b+1)**((2*n-1)-b) for b in range(2*n-1))[n-1])
%o # _Chai Wah Wu_, Sep 14 2014
%o (PARI) row(n) = vecsort(vector(n, k, k^(n-k+1))); \\ A247358
%o a(n) = row(2*n-1)[n]; \\ _Michel Marcus_, Jan 24 2022
%Y Cf. A247358, A000169.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Sep 14 2014