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A079901 Triangle of powers, T(n,k) = n^k, 0 <= k <= n, read by rows.

%I A079901 #22 May 09 2025 07:14:01
%S A079901 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 A079901 1296,7776,46656,1,7,49,343,2401,16807,117649,823543,1,8,64,512,4096,
%U A079901 32768,262144,2097152,16777216,1,9,81,729,6561,59049,531441,4782969,43046721
%N A079901 Triangle of powers, T(n,k) = n^k, 0 <= k <= n, read by rows.
%C A079901 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 A079901 Reinhard Zumkeller, <a href="/A079901/b079901.txt">Rows n = 0..125 of triangle, flattened</a>
%F A079901 T(n,k) = if k=0 then 1 else T(n,k-1)*n.
%F A079901 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.
%F A079901 T(n,n-2) = A000272(n) for n>2; T(n,n-1) = A000169(n) for n>1; T(n,n) = A000312(n).
%e A079901 Triangle begins:
%e A079901   1;
%e A079901   1,1;
%e A079901   1,2,4;
%e A079901   1,3,9,27;
%e A079901   1,4,16,64,256;
%e A079901   1,5,25,125,625,3125;
%t A079901 Join[{1},Flatten[Table[n^k,{n,9},{k,0,n}]]] (* _Harvey P. Dale_, Feb 08 2013 *)
%o A079901 (Haskell)
%o A079901 a079901 n k = a079901_tabl !! n !! k
%o A079901 a079901_row n = a079901_tabl !! n
%o A079901 a079901_tabl = zipWith (map . (^)) [0..] a002262_tabl
%o A079901 -- _Reinhard Zumkeller_, Mar 31 2015
%o A079901 (PARI) row(n) = vector(n+1, k, n^(k-1)); \\ _Amiram Eldar_, May 09 2025
%Y A079901 Cf. A107045/A107046 (matrix inverse).
%Y A079901 Cf. A002262, A000290, A000578, A000583, A000272, A000169, A000312.
%K A079901 nonn,easy,tabl
%O A079901 0,5
%A A079901 _Reinhard Zumkeller_, Feb 21 2003