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A229213 Square array of denominators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals. 1
1, 2, 4, 3, 16, 27, 4, 36, 216, 256, 5, 64, 729, 4096, 3125, 6, 100, 1728, 20736, 100000, 46656, 7, 144, 3375, 65536, 759375, 2985984, 823543, 8, 196, 5832, 160000, 3200000, 34012224, 105413504, 16777216, 9, 256 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Limit(t(n,k), n -> infinity) = exp(1/k).

1st row = A000027

2nd row = A016742

3rd row = A016767

4th row = A016804

5th row = A016853

1st column = A000312

2nd column = A062971

3rd column = A091482

4th column = A091483

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

Table of fractions begins:

   2,       3/2,        4/3,         5/4, ...

  9/4,     25/16,      49/36,       81/64, ...

64/27,   343/216,   1000/729,    2197/1728, ...

625/256, 6561/4096, 28561/20736, 83521/65536, ...

...

Table of denominators begins:

1,      2,     3,     4, ...

4,     16,    36,    64, ...

27,   216,   729,  1728, ...

256, 4096, 20736, 65536, ...

...

Triangle of antidiagonals begins:

1;

2, 4;

3, 16, 27;

4, 36, 216, 256;

...

MATHEMATICA

t[n_, k_] := (1+1/(k*n))^n; Table[t[n-k+1, k], {n, 1, 9}, {k, n, 1, -1}] // Flatten // Denominator

CROSSREFS

Cf. A229212(numerators), A016742, A016767, A016804, A016853, A000312, A062971, A091482, A091483.

Sequence in context: A053124 A242500 A132049 * A071970 A182103 A303053

Adjacent sequences:  A229210 A229211 A229212 * A229214 A229215 A229216

KEYWORD

frac,tabl,nonn

AUTHOR

Jean-Fran├žois Alcover, Sep 16 2013

STATUS

approved

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Last modified April 20 19:13 EDT 2021. Contains 343137 sequences. (Running on oeis4.)