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A303990
Triangle, read by rows: n^k * k^n, for n >= 1 and k = 1..n.
3
1, 2, 16, 3, 72, 729, 4, 256, 5184, 65536, 5, 800, 30375, 640000, 9765625, 6, 2304, 157464, 5308416, 121500000, 2176782336, 7, 6272, 750141, 39337984, 1313046875, 32934190464, 678223072849, 8, 16384, 3359232, 268435456, 12800000000, 440301256704, 12089663946752, 281474976710656
OFFSET
1,2
COMMENTS
Due to the symmetry of n^k * k^n under the exchange n <-> k, it is sufficient to consider n >= 1, and k = 1..n.
For the array n^k * k^n, with n >= 0 and k >= 0, read by antidiagonals, see the triangle A062275.
Thanks go to S. Heinemeyer for leading me to look at this.
The row sums give A303991.
FORMULA
T(n, k) = n^k * k^n, for n >= 1, k = 1..n.
EXAMPLE
The triangle T(n, k) begins:
======================================================================
n\k | 1 2 3 4 5 6 7 ...
----+-----------------------------------------------------------------
1: | 1
2: | 2 16
3: | 3 72 729
4: | 4 256 5184 65536
5: | 5 800 30375 640000 9765625
6: | 6 2304 157464 5308416 121500000 2176782336
7: | 7 6272 750141 39337984 1313046875 32934190464 678223072849
...
row n=8: 8, 16384, 3359232, 268435456, 12800000000, 440301256704, 12089663946752, 281474976710656;
row n=9: 9, 41472, 14348907, 1719926784, 115330078125, 5355700839936, 193010051319183, 5777633090469888, 150094635296999121;
row n=10: 10, 102400, 59049000, 10485760000, 976562500000, 60466176000000, 2824752490000000, 107374182400000000, 3486784401000000000, 100000000000000000000;
...
MATHEMATICA
Table[n^k k^n, {n, 10}, {k, n}] //Flatten (* Vincenzo Librandi, May 23 2018 *)
PROG
(Magma) /* As triangle */ [[n^k*k^n: k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, May 23 2018
(PARI) T(n, k) = n^k * k^n;
tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 25 2018
CROSSREFS
Sequence in context: A254637 A197226 A141239 * A095860 A070654 A036164
KEYWORD
nonn,tabl,easy
AUTHOR
Wolfdieter Lang, May 22 2018
STATUS
approved