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

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, 1296, 7776, 46656, 1, 7, 49, 343, 2401, 16807, 117649, 823543, 1, 8, 64, 512, 4096, 32768, 262144, 2097152, 16777216, 1, 9, 81, 729, 6561, 59049, 531441, 4782969, 43046721

Offset: 0

Author

Reinhard Zumkeller, Feb 21 2003

Keywords

• nonn
• easy
• tabl

Comments

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

Examples

			Triangle begins:
  1;
  1,1;
  1,2,4;
  1,3,9,27;
  1,4,16,64,256;
  1,5,25,125,625,3125;
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Crossrefs

Cf. A107045/A107046 (matrix inverse).

Cf. A002262, A000290, A000578, A000583, A000272, A000169, A000312.

Programs

Haskell

a079901 n k = a079901_tabl !! n !! k
a079901_row n = a079901_tabl !! n
a079901_tabl = zipWith (map . (^)) [0..] a002262_tabl
-- Reinhard Zumkeller, Mar 31 2015

Mathematica

Join[{1},Flatten[Table[n^k,{n,9},{k,0,n}]]] (* Harvey P. Dale, Feb 08 2013 *)

PARI

row(n) = vector(n+1, k, n^(k-1)); \\ Amiram Eldar, May 09 2025

Formula

T(n,k) = if k=0 then 1 else T(n,k-1)*n.

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.

T(n,n-2) = A000272(n) for n>2; T(n,n-1) = A000169(n) for n>1; T(n,n) = A000312(n).