A079901 - OEIS

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

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OFFSET

0,5

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

LINKS

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

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).

EXAMPLE

Triangle begins:

1,1;

1,2,4;

1,3,9,27;

1,4,16,64,256;