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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
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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
*
A356063
A071970
A387554
Adjacent sequences:
A229210
A229211
A229212
*
A229214
A229215
A229216
KEYWORD
frac
,
tabl
,
nonn
AUTHOR
Jean-François Alcover
, Sep 16 2013
STATUS
approved
