A155955 Triangle read by rows: T(n,k) = (k*n)^k, 0 <= k <= n.

1, 1, 1, 1, 2, 16, 1, 3, 36, 729, 1, 4, 64, 1728, 65536, 1, 5, 100, 3375, 160000, 9765625, 1, 6, 144, 5832, 331776, 24300000, 2176782336, 1, 7, 196, 9261, 614656, 52521875, 5489031744, 678223072849, 1, 8, 256, 13824, 1048576, 102400000, 12230590464

Offset: 0

Author

Reinhard Zumkeller, Jan 31 2009

Keywords

• nonn
• tabl

Comments

T(n,0) = 1;

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

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

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

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

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

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

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

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

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

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

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

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

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

Examples

			Triangle begins:
  1;
  1, 1;
  1, 2,  16;
  1, 3,  36,  729;
  1, 4,  64, 1728,  65536;
  1, 5, 100, 3375, 160000,  9765625;
  1, 6, 144, 5832, 331776, 24300000, 2176782336;
  ...
		

Links

• G. C. Greubel, Rows n=0..100 of triangle, flattened

Crossrefs

Cf. A000312.

Programs

Magma

[[(n*k)^k: k in [0..n]]: n in [0..10]]; // G. C. Greubel, Sep 15 2018

Mathematica

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 *)

PARI

for(n=0,10, for(k=0,n, print1((k*n)^k, ", "))) \\ G. C. Greubel, Sep 15 2018