OFFSET
1,2
COMMENTS
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
KEYWORD
AUTHOR
Wolfdieter Lang, May 22 2018
STATUS
approved