A229213 Square array of denominators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals.

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

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 A182103

Adjacent sequences: A229210 A229211 A229212 * A229214 A229215 A229216

Keyword

frac,tabl,nonn

Author

Jean-François Alcover, Sep 16 2013

Status

approved