A247363 Central terms of triangle A247358.

1, 3, 16, 64, 343, 4096, 59049, 1000000, 14348907, 129140163, 1475789056, 38443359375, 1099511627776, 34271896307633, 1156831381426176, 42052983462257059, 1152921504606846976, 18446744073709551616, 295147905179352825856, 12116574790945106558976

Offset

1,2

Comments

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.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..400

Formula

a(n) = A247358(2*n-1,n).

Example

.   n |        a(n) | b(n)^e(n) | b(n)+e(n)
. ----+-------------+-----------+----------
.   1 |           1 |    1^1    |     2
.   2 |           3 |    3^1    |     4
.   3 |          16 |    2^4    |     6
.   4 |          64 |    2^6    |     8
.   5 |         343 |    7^3    |    10
.   6 |        4096 |    8^4    |    12
.   7 |       59049 |    9^5    |    14
.   8 |     1000000 |   10^6    |    16
.   9 |    14348907 |    3^15   |    18
.  10 |   129140163 |    3^17   |    20
.  11 |  1475789056 |   14^8    |    22
.  12 | 38443359375 |   15^9    |    24

Prog

(Haskell)
a247363 n = a247358 (2 * n - 1) n
(Python)
def A247363(n):
....return(sorted((b+1)**((2*n-1)-b) for b in range(2*n-1))[n-1])
# Chai Wah Wu, Sep 14 2014
(PARI) row(n) = vecsort(vector(n, k, k^(n-k+1))); \\ A247358
a(n) = row(2*n-1)[n]; \\ Michel Marcus, Jan 24 2022

Crossrefs

Cf. A247358, A000169.

Sequence in context: A323941 A267036 A037451 * A007143 A359176 A062960

Adjacent sequences: A247360 A247361 A247362 * A247364 A247365 A247366

Keyword

nonn

Author

Reinhard Zumkeller, Sep 14 2014

Status

approved