|
%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
|
