This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A303990 #19 Sep 08 2022 08:46:21 %S A303990 1,2,16,3,72,729,4,256,5184,65536,5,800,30375,640000,9765625,6,2304, %T A303990 157464,5308416,121500000,2176782336,7,6272,750141,39337984, %U A303990 1313046875,32934190464,678223072849,8,16384,3359232,268435456,12800000000,440301256704,12089663946752,281474976710656 %N A303990 Triangle, read by rows: n^k * k^n, for n >= 1 and k = 1..n. %C A303990 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. %C A303990 For the array n^k * k^n, with n >= 0 and k >= 0, read by antidiagonals, see the triangle A062275. %C A303990 Thanks go to S. Heinemeyer for leading me to look at this. %C A303990 The row sums give A303991. %F A303990 T(n, k) = n^k * k^n, for n >= 1, k = 1..n. %e A303990 The triangle T(n, k) begins: %e A303990 ====================================================================== %e A303990 n\k | 1 2 3 4 5 6 7 ... %e A303990 ----+----------------------------------------------------------------- %e A303990 1: | 1 %e A303990 2: | 2 16 %e A303990 3: | 3 72 729 %e A303990 4: | 4 256 5184 65536 %e A303990 5: | 5 800 30375 640000 9765625 %e A303990 6: | 6 2304 157464 5308416 121500000 2176782336 %e A303990 7: | 7 6272 750141 39337984 1313046875 32934190464 678223072849 %e A303990 ... %e A303990 row n=8: 8, 16384, 3359232, 268435456, 12800000000, 440301256704, 12089663946752, 281474976710656; %e A303990 row n=9: 9, 41472, 14348907, 1719926784, 115330078125, 5355700839936, 193010051319183, 5777633090469888, 150094635296999121; %e A303990 row n=10: 10, 102400, 59049000, 10485760000, 976562500000, 60466176000000, 2824752490000000, 107374182400000000, 3486784401000000000, 100000000000000000000; %e A303990 ... %t A303990 Table[n^k k^n, {n, 10}, {k, n}] //Flatten (* _Vincenzo Librandi_, May 23 2018 *) %o A303990 (Magma) /* As triangle */ [[n^k*k^n: k in [1..n]]: n in [1.. 15]]; // _Vincenzo Librandi_, May 23 2018 %o A303990 (PARI) T(n, k) = n^k * k^n; %o A303990 tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); print); \\ _Michel Marcus_, May 25 2018 %Y A303990 Cf. A062275, A303991. %K A303990 nonn,tabl,easy %O A303990 1,2 %A A303990 _Wolfdieter Lang_, May 22 2018