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%I #14 Mar 31 2015 20:21:38
%S 1,1,1,1,2,4,1,3,9,27,1,4,16,64,256,1,5,25,125,625,3125,1,6,36,216,
%T 1296,7776,46656,1,7,49,343,2401,16807,117649,823543,1,8,64,512,4096,
%U 32768,262144,2097152,16777216,1,9,81,729,6561,59049,531441,4782969,43046721
%N Triangle of powers, T(n,k) = n^k, 0<=k<=n, read by rows.
%C T(n,k) = if k=0 then 1 else T(n,k-1)*n;
%C T(n,0)=1; T(n,1)=n for n>0; T(n,2)=A000290(n) for n>1; T(n,3)=A000578(n) for n>2; T(n,4)=A000583(n) for n>3;
%C T(n,n-2)=A000272(n) for n>2; T(n,n-1)=A000169(n) for n>1; T(n,n)=A000312(n).
%C Matrix inverse equals the triangle R where R(n,k) = A107045(n,k)/A107046(n,k) are coefficients with exponential-like properties. - _Paul D. Hanna_, May 22 2005
%H Reinhard Zumkeller, <a href="/A079901/b079901.txt">Rows n = 0..125 of triangle, flattened</a>
%e 1;
%e 1,1;
%e 1,2,4;
%e 1,3,9,27;
%e 1,4,16,64,256;
%e 1,5,25,125,625,3125;
%t Join[{1},Flatten[Table[n^k,{n,9},{k,0,n}]]] (* _Harvey P. Dale_, Feb 08 2013 *)
%o (Haskell)
%o a079901 n k = a079901_tabl !! n !! k
%o a079901_row n = a079901_tabl !! n
%o a079901_tabl = zipWith (map . (^)) [0..] a002262_tabl
%o -- _Reinhard Zumkeller_, Mar 31 2015
%Y Cf. A107045/A107046 (matrix inverse).
%Y Cf. A002262, A000290, A000578, A000583, A000272, A000169, A000312.
%K nonn,easy,tabl
%O 0,5
%A _Reinhard Zumkeller_, Feb 21 2003
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