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A089072 Triangle read by rows: T(n,k) = k^n, n>=1, 1<=k<=n. 9
1, 1, 4, 1, 8, 27, 1, 16, 81, 256, 1, 32, 243, 1024, 3125, 1, 64, 729, 4096, 15625, 46656, 1, 128, 2187, 16384, 78125, 279936, 823543, 1, 256, 6561, 65536, 390625, 1679616, 5764801, 16777216, 1, 512, 19683, 262144, 1953125, 10077696, 40353607 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

T(n, k) = number of mappings from an n-element set into a k-element set. - Clark Kimberling, Nov 26 2004

LINKS

Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened

FORMULA

Set T = round(sqrt(2*n),0) then a(n) = (n+T*(1-T)/2)^T. - Gerald Hillier, Apr 12 2015

T(n,k) = A051129(n,k). - R. J. Mathar, Dec 10 2015

EXAMPLE

Triangle begins:

1

1 4

1 8 27

1 16 81 256

1 32 243 1024 3125

1 64 729 4096 15625 46656

MATHEMATICA

Column[Table[k^n, {n, 8}, {k, n}], Center] (* Alonso del Arte, Nov 14 2011 *)

PROG

(Haskell)

a089072 = flip (^)

a089072_row n = map (a089072 n) [1..n]

a089072_tabl = map a089072_row [1..]  -- Reinhard Zumkeller, Mar 18 2013

CROSSREFS

Related to triangle of Eulerian numbers A008292.

Row sums are A031971.

T(n,n) = A000312(n).

Sequence in context: A297194 A077910 A100235 * A036177 A177841 A141680

Adjacent sequences:  A089069 A089070 A089071 * A089073 A089074 A089075

KEYWORD

easy,nonn,tabl

AUTHOR

Alford Arnold, Dec 04 2003

EXTENSIONS

More terms and better definition from Herman Jamke (hermanjamke(AT)fastmail.fm), Jul 10 2004

Offset corrected by Reinhard Zumkeller, Mar 18 2013

STATUS

approved

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Last modified February 20 15:02 EST 2018. Contains 299380 sequences. (Running on oeis4.)