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

0,5

Comments

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).

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A107045/A107046 (matrix inverse).

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

Sequence in context: A100075 A059836 A069270 * A121426 A190183 A004515

Adjacent sequences: A079898 A079899 A079900 * A079902 A079903 A079904

Keyword

nonn,easy,tabl

Author

Reinhard Zumkeller, Feb 21 2003

Status

approved