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Triangle read by rows: T(n,k) = (k*n)^k, 0 <= k <= n.
15

%I #11 Sep 08 2022 08:45:41

%S 1,1,1,1,2,16,1,3,36,729,1,4,64,1728,65536,1,5,100,3375,160000,

%T 9765625,1,6,144,5832,331776,24300000,2176782336,1,7,196,9261,614656,

%U 52521875,5489031744,678223072849,1,8,256,13824,1048576,102400000,12230590464

%N Triangle read by rows: T(n,k) = (k*n)^k, 0 <= k <= n.

%C T(n,0) = 1;

%C T(n,1) = n for n > 0;

%C T(n,2) = A016742(n) for n > 1;

%C T(n,3) = A016767(n) for n > 2;

%C T(n,4) = A016804(n) for n > 3;

%C T(n,5) = A016853(n) for n > 4;

%C T(n,6) = A016914(n) for n > 5;

%C T(n,7) = A016987(n) for n > 6;

%C T(n,8) = A017072(n) for n > 7;

%C T(n,9) = A017169(n) for n > 8;

%C T(n,10) = A017278(n) for n > 9;

%C T(n,11) = A017399(n) for n > 10;

%C T(n,12) = A017532(n) for n > 11;

%C T(n,n) = A062206(n).

%H G. C. Greubel, <a href="/A155955/b155955.txt">Rows n=0..100 of triangle, flattened</a>

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 2, 16;

%e 1, 3, 36, 729;

%e 1, 4, 64, 1728, 65536;

%e 1, 5, 100, 3375, 160000, 9765625;

%e 1, 6, 144, 5832, 331776, 24300000, 2176782336;

%e ...

%t Table[If[n == 0, 1, If[ k == 0, 1, (k*n)^k]], {n, 0, 10}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Sep 15 2018 *)

%o (PARI) for(n=0,10, for(k=0,n, print1((k*n)^k, ", "))) \\ _G. C. Greubel_, Sep 15 2018

%o (Magma) [[(n*k)^k: k in [0..n]]: n in [0..10]]; // _G. C. Greubel_, Sep 15 2018

%Y Cf. A000312.

%K nonn,tabl

%O 0,5

%A _Reinhard Zumkeller_, Jan 31 2009