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A247363 Central terms of triangle A247358.

%I A247363 #18 May 22 2025 10:21:40
%S A247363 1,3,16,64,343,4096,59049,1000000,14348907,129140163,1475789056,
%T A247363 38443359375,1099511627776,34271896307633,1156831381426176,
%U A247363 42052983462257059,1152921504606846976,18446744073709551616,295147905179352825856,12116574790945106558976
%N A247363 Central terms of triangle A247358.
%C A247363 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 A247363 Reinhard Zumkeller, <a href="/A247363/b247363.txt">Table of n, a(n) for n = 1..400</a>
%F A247363 a(n) = A247358(2*n-1,n).
%e A247363 .   n |        a(n) | b(n)^e(n) | b(n)+e(n)
%e A247363 . ----+-------------+-----------+----------
%e A247363 .   1 |           1 |    1^1    |     2
%e A247363 .   2 |           3 |    3^1    |     4
%e A247363 .   3 |          16 |    2^4    |     6
%e A247363 .   4 |          64 |    2^6    |     8
%e A247363 .   5 |         343 |    7^3    |    10
%e A247363 .   6 |        4096 |    8^4    |    12
%e A247363 .   7 |       59049 |    9^5    |    14
%e A247363 .   8 |     1000000 |   10^6    |    16
%e A247363 .   9 |    14348907 |    3^15   |    18
%e A247363 .  10 |   129140163 |    3^17   |    20
%e A247363 .  11 |  1475789056 |   14^8    |    22
%e A247363 .  12 | 38443359375 |   15^9    |    24
%o A247363 (Haskell)
%o A247363 a247363 n = a247358 (2 * n - 1) n
%o A247363 (Python)
%o A247363 def A247363(n):
%o A247363     return(sorted((b+1)**((2*n-1)-b) for b in range(2*n-1))[n-1])
%o A247363 # _Chai Wah Wu_, Sep 14 2014
%o A247363 (PARI) row(n) = vecsort(vector(n, k, k^(n-k+1))); \\ A247358
%o A247363 a(n) = row(2*n-1)[n]; \\ _Michel Marcus_, Jan 24 2022
%Y A247363 Cf. A247358, A000169.
%K A247363 nonn
%O A247363 1,2
%A A247363 _Reinhard Zumkeller_, Sep 14 2014